Dr. Rakesh Kumar

ContactInformation

Professor (Assistant)Department of Basic and Applied SciencesPunjabi University, Patiala-147 002, IndiaEmails: rakesh bas@pbi.ac.in; dr rk37c@yahoo.co.inContact No. +91-98154-30944

PersonalDetails

• Father’s Name: Sh. Mohan Lal

• Mother’s Name: Smt. Bhagwanti

• Marital Status: Married

• Spouses Name: Dr. Rachna Rani

• Date of Birth: 3rd December, 1977

ResearchInterests

• Differential Geometry with Indefinite Metrics.

• Geometry of Lightlike Submanifolds and Hypersurfaces of semi-RiemannianManifolds.

• Geometry of Indefinite Golden and Statistical Manifolds.

Education • Ph.D. degree under the supervision of Dr. R.K. Nagaich, Department ofMathematics, Punjabi University, Patiala with title Geometry of manifoldswith indefinite metrics, in December 2008.

• UGC-CSIR (NET) held on 22-06-2003 under Roll No. 403560 vide CSIRletter no. F.No.10-2(5)2003(I)-EU.II dated 01-11-2003.

• M.Sc. (Mathematics) from Punjabi University, Patiala, India, in April 2002.

Awards • Gold Medal for ranking first in M. Sc. Examination at Punjabi University,Patiala in April 2002.

• Junior Research Fellowship (JRF) by UGC-CSIR for pursuing Ph.D.

• Travel Grant by International Mathematical Union in collaboration with theInternational Congress of Mathematicians (ICM) Organizing Committee toattend ICM-2010 at Hyderabad during 19-27 August, 2010.

• Young Geometer Award by The Tensor Society, India in an InternationalConference on Differential Geometry and Relativity, organized by Departmentof Mathematics, Aligarh Muslim University, Aligarh, during 20-23 Nov., 2012.

• Best Paper Presentation Award in International Conference on MathematicalModeling and Statistical Analysis organized by Department of Mathematics,JC DAV College, Dasuya, Hoshiarpur, Punjab on September 30, 2014.

1 of 17

• Young Geometer Award by The Tensor Society, India in an InternationalConference on Differential Geometry and its Applications, organized by theDepartment of Mathematics, Jadavpur University, Kolkata, during 16-18 Oct.,2014.

• Travel Grant by Abdus Salam International Centre for Theoretical Physics,Trieste, Italy to attend School and Workshop on Complex Analysis, Geometryand Dynamics, at ICTP, Italy from September 21 to October 3, 2015.

• Outstanding Faculty Award for the contribution in the field of DifferentialGeometry by the Board of Management of the Venus International Foundationon July 9, 2016 at Chennai, India.

• Travel Grant with Letter No. ITS/812/2017-18 dated May 24, 2017 byScience and Engineering Research Board (SERB), Department of Science andTechnology (DST), Government of India, to deliver an invited talk in theconference Differential Geometry, organized by Institute of Mathematics ofthe Polish Academy of Sciences at The Mathematical Research and ConferenceCenter in Bedlewo, Poland, during June 18-24, 2017.

• Adarsh Vidya Saraswati Rashtriya Puraskar for contribution in Mathematicsby the Global Management Council, Glacier Journal Research Foundation,Ahmedabad, India, on 02 March, 2018.

• Travel Grant by International Mathematical Union in collaboration with theInternational Congress of Mathematicians (ICM) Organizing Committee toattend ICM-2018 at Rio de Janeiro, Brazil, during 01–09 August, 2018.

Honors • Member of Scientific Committee of 16th International Geometry Symposiumto be held at Manisa Celal Bayar University, Manisa, Turkey, during July4–7, 2018.

Ph. D ThesisSupervised/Supervising

• Mr. Manish GognaTopic: The Geometry of CR-Lightlike SubmanifoldsStatus: Awarded on July 8, 2013

• Mr. Varun JainTopic: The Geometry of GCR-Lightlike Submanifolds of Indefinite SasakianManifoldsStatus: Awarded on May 28, 2015

• Mr. Sangeet KumarTopic: The Geometry of GCR-Lightlike Submanifolds of Indefinite KaehlerManifoldsStatus: Awarded on May 28, 2015

• Ms. Rashmi SachdevaTopic: The Geometry of Slant Lightlike SubmanifoldsStatus: Awarded on November 9, 2016

• Ms Garima GuptaTopic: Geometry of Lightlike Submanifolds of semi-Riemannian ManifoldsStatus: Submitted on February 27, 2018

2 of 17

• Ms. RupaliTopic: Geometry of Lightlike SubmersionsStatus: Registered on February 27, 2015.

TeachingExperience

• Working as a Regular Assistant Professor (Mathematics) in the Departmentof Basic and Applied Sciences, Punjabi University, Patiala, from 6th June,2005 to till date.

• Worked as a Guest Faculty in Department of Statistics, Panjabi UniversityPatiala for teaching Calculus, Vector Analysis and Geometry to B.Sc. studentsfrom 2006 to 2010.

• Worked as a Guest Faculty in Department of Mathematics, Panjabi UniversityPatiala for teaching Discrete Mathematics to M. Sc. students from Jan. 2011to May 2011.

References forRecommendation

Prof. (Ex.) Dr. Zafar AhsanDepartment of MathematicsAligarh Muslim University, Aligarh, Indiazafar.ahsan@rediffmail.com; Contact No. +91- 98973-99337

Prof. Uday Chand DeDepartment of Pure MathematicsUniversity of Calcutta, Kolkata, Indiauc de@yahoo.com; Contact No.: +91-94335-33873

Prof. (Ex.) R. K. NagaichDepartment of MathematicsPunjabi University, Patiala-147 002. Indianagaich58rakesh@gmail.com; Contact No. +91- 94178-74900

Membership ofResearchBodies

• Life member of Punjab Academy of Sciences, India. Membership No. 1042.

• Life member of International Association of Mathematical Physics, Denmark.Membership No. 1851.

• Life member of The Tensor Society, India, Membership No. 69.

• Life member of International Association of Engineers, Hon Kong, MembershipNo. 113515.

• Life member of Ramanujan Mathematical Society, India, Membership No.1088.

• Senior member of the International Association of Computer Science andInformational Technology, Singapore. Membership No. 80345626.

• Department Teacher In-Charge of The National Programme on TechnologyEnhanced Learning (NPTEL) Local Chapter, Punjabi University, Patiala,India.

Editor/Reviewer ofthe Journals

• Reviewer of Mathematical Reviews, Reviewer No. 097544.

• Joint Editorial Secretary of Journal of The Tensor Society, India.

3 of 17

Invited Talks1. Delivered an invited talk on Geometry of Kaehler-Norden-Golden manifolds

and Harmonicity, in 22nd International Conference of InternationalAcademy of Physical Sciences (CONIAPS-XXII) on Recent Trendsin Physical Sciences, organized by Faculty of Science, Dr Ram ManoharLohia Avadh University, Faizabad during 13–15 April, 2018.

2. Delivered an extension lecture on An introduction to non-Euclidean geometry,organized by P.G. Department of Mathematics, Mohindra College, Patiala,on 26 March, 2018.

3. Delivered an invited talk on Recent developments of mathematics in higherstudies in the Internship Camp under INSPIRE (Innovation inScience Pursuit for Inspired Research) Program organized by ShantiDevi Arya Mahila College, Dinanagar, Distt Gurdaspur, Punjab during 14-18 December, 2017.

4. Delivered an invited talk on Radical screen transversal lightlike submanifoldsof indefinite Kaehler manifolds admitting a quarter-symmetric non-metricconnection in National Conference on Differential Geometry andGeneral Relativity organized Department of Mathematics, Sardar PatelUniversity, Vallabh Vidyanagar, Gujrat, during 28-29 November, 2017.

5. Delivered an invited talk on Geometry of real half lightlike submanifolds ofindefinite Kaehler manifolds in the 2nd National Conference on Roleof Mathematics and Computer Science in Advancement of Physicsorganized Government Degree College, Kathua during 10-11 November,2017.

6. Delivered an invited talk on Geometry of radical screen transversal lightlikesubmanifolds of indefinite Kaehler manifolds in the 21st InternationalConference of the International Academy of Physical Sciences(CONIAPS-XXI) on Symbiotic Development of Mathematical,Physical, Chemical and Computational Sciences organized by theDepartment of Mathematics, Guru Jambheshwar University, Hissar during28-30 October, 2017.

7. Delivered a keynote lecture in the One Week National Workshop onLATEX and Matlab: Indispensable Tools for Researchers, organizedby Department of Applied Science, Guru Kashi University, Talwandi Sabo,Bathinda on August 1, 2017.

8. Delivered an expert talk on Effective technical writing using LATEX in OneWeek Faculty Development Program, organized by Department ofComputer Science and Engg., Baba Banda Singh Bahadur EngineeringCollege, Fatehgarh Sahib on July 3, 2017.

9. Delivered an invited talk On geometry of real half lightlike submanifolds ofindefinite Kaehler manifolds with quarter symmetric metric connection inConference Differential Geometry organized by the Institute of Math-ematics of the Polish Academy of Sciences at The Mathematical Researchand Conference Center, Bedlewo, Poland during 18-24 June, 2017.

4 of 17

10. Delivered an invited talk on Curves and surfaces in National Workshopon Advanced Computational Mathematics and its Applications,organized by Department of Mathematics, Guru Nanak College, Budhladaduring 24-25 April, 2017.

11. Delivered an invited talk on Half lightlike submanifolds of indefinite Kaehlermanifolds in National Conference on Topology, Analysis, Algebraand Their Applications, organized by Department of Mathematics, ShriMata Vaishno Devi University, Katra during 7-8 March, 2017.

12. Delivered an extension lecture on Role of differential geometry in daily lifeat S. C. D. Government College, Ludhiana on February 27th, 2017.

13. Delivered an invited talk on The applications of Numerical Methods inthe Centre for Mathematics and Statistics, Central University of Punjab,Bathinda on February 15, 2017.

14. Chaired and delivered an invited talk on Real half lightlike submanifolds ofindefinite Kaehler manifolds with quarter symmetric metric connection inNational Conference on Differential Geometry & Its Applications,organized by Department of Mathematics and Statistics, D.D.U. University,Gorakhpur during 27-28 January, 2017.

15. Delivered an expert talk on Numerical methods in Workshop for PGStudents, Mata Gujri College Fathegarh Sahib, Punjab on December 13,2016.

16. Delivered an invited talk on The geometry of lightlike submanifolds of semi-Riemannian manifolds in International Conference on Mathem-aticsfor Brain Studies, organized by School of Sciences, Center for ResearchStudies, Noida International University, Greater Noida, during 1-3 February,2016.

17. Delivered an extension lecture on Solution of algebraic and transcendentalequations, organized by the PG Department of Mathematics, GovernmentMahindra College, Patiala on December 4, 2015.

18. Delivered an invited talk on Lightlike submanifolds of semi-Riemannianmanifolds in 81st Annual Conference of The Indian MathematicalSociety, organized by Department of Mathematics and Department ofComputer Science & Engineering, Visvesvaraya National Institute of Techn-ology, Nagpur, India, during December 27-30, 2015.

19. Delivered an expert talks on Real analysis in One week Faculty Develo-pment Program, organized by the University School of Engineering andTechnology, Rayat-Bahra University, Mohali, during June 15-19, 2015.

20. Delivered an expert Lecture on Application of Latex in paper writing inUGC sponsored National Workshop on Research Tools in Mathe-matics, organized by PG Department of Mathematics, Mata Gujri College,Sri Fathegarh Sahib, Punjab, India on December 24, 2014.

5 of 17

21. Delivered an expert Lecture on Introduction of Latex in research in UGCsponsored National Workshop on Research Tools in Mathematics,organized by PG Department of Mathematics, Mata Gujri College, SriFathegarh Sahib, Punjab, India, on December 23, 2014.

22. Delivered two expert talks on Laplace transform in Faculty DevelopmentProgram on Engineering Mathematics, organized by Rayat-BahraInst-itute of Engineering and Bio-Technology, Mohali on July 18, 2014.

23. Delivered invited talks on LATEXSoftware in Refresher Course in Mathe-matics, organized by University Institute of Engineering, Chandigarh Univ-ersity, Mohali during July 7-12, 2014.

24. Chaired Lab Sessions in National Workshop on LATEX, organized by Schoolof Applied Sciences, Chitkara University, Rajpura during July 8-10, 2013.

RefereedJournalPublications

1. Garima Gupta, Rashmi Sachdeva, Rakesh Kumar∗ and R. K. Nagaich,Pointwise slant lightlike submanifolds of indefinite Kaehler manifolds,Mediterr. J. Math., (2018) 15:105, 1–17. (SCI & SCOPUS Indexed)

2. Garima Gupta, Rakesh Kumar∗ and R. K. Nagaich, Radical screen transv-ersal lightlike submanifolds of indefinite Kaehler manifolds admitting aquarter-symmetric non-metric connection, Int. J. Geom. Methods Mod.Phys., 15 (2018), 1–21. (SCI & SCOPUS Indexed)

3. Rashmi Sachdeva, Rachna Rani, Rakesh Kumar∗ and S. S. Bhatia, Studyof totally contact umbilical hemi-slant lightlike submanifolds of indefiniteSasakian manifolds, Balkan J. Geom. Appl., 22 (1) (2017), 70–80. (SCI &SCOPUS Indexed) (MR3678011)

4. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Totally umbilicalslant lightlike submanifolds of indefinite Kaehler manifolds, KyungpookMath. J., 57 (2017), 503–516. (SCOPUS Indexed)

5. Varun Jain, Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Somecharacterization theorems on holomorphic sectional curvature of GCR light-like submanifolds, Int. J. Geom. Methods Mod. Phys., 14 (3), (2017), 1–18.(SCI & SCOPUS Indexed) (MR3608891)

6. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, The axioms of indefi-nite hemi-slant planes and spheres, Lobachevskii J. Math., 38 (1) (2017),125-130. (SCOPUS Indexed) (MR3615333)

7. Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, The axioms of spheresin lightlike geometry of submanifolds, Proc. Indian Acad. Sci. (Math.Sci), 126 (4) (2016), 613–621. (SCI & SCOPUS Indexed) (MR3568253)

8. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Slant lightlike subm-ersions from indefinite almost Hermitian manifold onto a lightlike manifold,Ukrainian Math. J., 68 (7) (2016), 963–971. (SCI & SCOPUS Indexed)(MR3552040)

∗Corresponding Author

6 of 17

9. Rachna Rani, Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, Chara-cterizations of null holomorphic sectional curvature of GCR-lightlike sub-manifold of an indefinite nearly Kaehler manifold, Anal. Theory Appl., 32(2) (2016), 122–134. (MR3529324)

10. Garima Gupta, Rakesh Kumar∗ and R. K. Nagaich, Screen conformallightlike submanifolds of semi-Riemannian manifolds, J. Geometry, 107(2016), 635–655. (SCOPUS Indexed) (MR3563217)

11. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Warped productslant lightlike submanifolds of indefinite Sasakian manifolds, Balkan J.Geom. Appl., 20 (1) (2015), 98–108. (SCI & SCOPUS Indexed) (MR3367070)

12. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Totally contactumbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds,Tamkang J. Maths., 46 (2015), 179–191. (SCOPUS Indexed) (MR3352356)

13. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Totally umbilicalhemi-slant lightlike submanifolds, New York J. Math., 21 (2015), 191–203.(SCI & SCOPUS Indexed) (MR3336552)

14. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Non existence of totallycontact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu mani-folds, Hacet. J. Math. Stat., 44 (1) (2015), 83–91. (SCI & SCOPUSIndexed) (MR3363766)

15. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Non existence oftotally umbilical proper slant lightlike submanifold of indefinite Sasakianmanifolds, Bull. Iranian Math. Soc., 40 (5) (2014), 1135–1151. (SCI &SCOPUS Indexed) (MR3273829)

16. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, Ricci Tensor forGCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, Afr.Diaspora J. Math., 17 (1) (2014), 32-48. (MR3270011)

17. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, GCR-lightlike sub-manifolds of a semi-Riemannian product manifold, Bull. Korean Math.Soc., 51 (3) (2014), 883-899. (SCI & SCOPUS Indexed) (MR3214253)

18. Manish Gogna, Rakesh Kumar∗ and R. K. Nagaich, On totally contactumbilical CR-lightlike submanifolds of indefinite Sasakian manifolds, Dem-onstratio Math., 47 (1) (2014), 170–178. (ESCI & SCOPUS Indexed)(MR3200194)

19. Rakesh Kumar∗, Rachna Rani, Manish Gogna and R. K. Nagaich, Ch-aracterization of GCR-lightlike warped product of indefinite Sasakian man-ifolds, Arab J. Math. Sci., 20 (4) (2014), 191–204. (MR3227418)

20. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, GCR-lightlike subm-anifolds of indefinite nearly Kaehler manifolds, Bull. Korean Math. Soc.,50 (4) (2013), 1173-1192. (SCI & SCOPUS Indexed) (MR3092381)

7 of 17

21. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Totally contactumbilical hemi-slant lightlike submanifold of an indefinite Cosymplecticmanifold, Proceedings of International Conference on Information and Mat-hematical Sciences, Baba Farid College of Engineering and Technology,Bathinda, Punjab, during 24-26 October, 2013, 146–149.

22. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Integrability of thedistributions in GCR-lightlike submanifolds, Mathematical Sciences andApplications E-Notes, 1 (2) (2013), 1–10.

23. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, Ricci tensor of GCR-lightlike submanifolds of indefinite complex space, Bull. Iranian Math.Soc., 39 (5) (2013), 1009–1029. (SCI & SCOPUS Indexed) (MR3126270)

24. Rakesh Kumar, Characterization of the GCR-lightlike warped productof indefinite Kenmotsu manifolds, Mat. Vesnik, 65 (4) (2013), 533–546.(SCOPUS Indexed) (MR3101437)

25. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Integrability of thedistributions in GCR-lightlike submanifolds of indefinite Sasakian manifolds,Kyungpook Math. J., 53 (2) (2013), 207–218. (SCOPUS Indexed)

26. Rashmi Sachdeva, Rakesh Kumar∗ and S. S. Bhatia, Totally contactumbilical slant lightlike submanifolds of indefinite Cosymplectic manifolds,ISRN Geometry, Volume 2013, Article ID 231869, 1–8. (MR3095653)

27. Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Totally contact umbilicallightlike hypersurfaces of indefinite S-manifolds, Journal of Mathematics,Volume 2013, Article ID 395787, 1–7. (MR3097212)

28. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Non existence of totallycontact umbilical GCR-lightlike submanifolds of indefinite Cosymplecticmanifolds, Vietnam J. Math., 41 (2013), 121–134. (SCOPUS Indexed)(MR3089811)

29. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Integrability of thedistributions in GCR-lightlike submanifolds of indefinite Cosymplectic man-ifolds, Lobachevskii J. Math., 34 (1) (2013), 76–84. (SCOPUS Indexed)(MR3031558)

30. Rakesh Kumar∗ and R. K. Nagaich, Characterization of GCR-lightlikewarped product of indefinite Cosymplectic manifolds, Novi Sad J. Math.,42 (2) (2012), 111–126. (MR3099741)

31. Manish Gogna, Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Totallyumbilical lightlike hypersurfaces of semi-Riemannian manifolds, J. TensorSoc., 6 (2) (2012), 145–156. (MR3076205)

32. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, On GCR-lightlike productof Indefinite Cosymplectic manifolds, Int. J. Math. Math. Sci., Volume2012, Article ID 605816, 1–12. (SCOPUS Indexed) (MR2959591)

8 of 17

33. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, Characterizationof holomorphic bisectional curvature of GCR-lightlike submanifolds, Adv.Math. Phys., Volume 2012, Article ID 356263, 1–18. (SCI & SCOPUSIndexed) (MR2945124)

34. Sangeet Kumar, Rakesh Kumar∗ and R. K. Nagaich, Integrebility ofdistributions in GCR-lightlike submanifolds of indefinite Kaehler manifolds,Commun. Korean Math. Soc., 27 (3) (2012), 591–602. (SCOPUS Indexed)(MR2978726)

35. Manish Gogna, Rakesh Kumar∗ and R. K. Nagaich, Integrability of thedistributions in CR-lightlike submanifolds of indefinite Sasakian manifolds,Int. J. Math. Anal., 6 (2012), 199–207. (SCOPUS Indexed) (MR2876191)

36. Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Characterization of CRlightlike warped product of indefinite Kaehler manifolds, ISRN Mathemat-ical Physics, Volume 2012, Article ID 957176, 1–14.

37. Manish Gogna, Rakesh Kumar∗ and R. K. Nagaich, Generalized CauchyRiemann lightlike submanifolds, J. Math. Anal., 2 (2) (2011), 29–37.(MR2877998)

38. Rakesh Kumar∗, R. K. Nagaich and J. B. Jun, Vanishing of the Bochnercurvature tensor of indefinite almost Hermitian manifolds, Eurasian Math.J., 2 (3) (2011), 82–88. (MR2910842)

39. Rakesh Kumar∗, Sanget Kumar and R. K. Nagaich, GCR lightlike productof indefinite Kaehler manifolds, ISRN Geometry, Volume 2011, Article ID531281, 1–13.

40. Varun Jain, Rakesh Kumar∗ and R. K. Nagaich, Totally contact umbilicalGCR-lightlike submanifolds of indefinite Sasakian manifolds, Vietnam J.Math., 39 (1) (2011), 91-103. (SCOPUS Indexed) (MR2841638)

41. Rakesh Kumar∗, Varun Jain and R. K. Nagaich, GCR-lightlike productof indefinite Sasakian manifolds, Adv. Math. Phys., Volume 2011, ArticleID 983069, 1–13. (SCI & SCOPUS Indexed) (MR2801348)

42. Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Indefinite nearlyKahler manifolds of constant type, Eurasian Math. J., 2 (1) (2011), 120–127. (MR2910825)

43. Rakesh Kumar∗, Jasleen Kaur and R. K. Nagaich, On CR lightlikeproduct of an indefinite Kaehler manifold, Int. J. Math. Math. Sci.,Volume 2011, Article ID 857953, 1–10. (SCOPUS Indexed) (MR2793387)

44. Rakesh Kumar∗, Rachna Rani and R. K. Nagaich, On contact CR-lightlike submanifolds of indefinite Sasakian manifolds, Vietnam J. Math.,38 (4) (2010), 485–499. (SCOPUS Indexed) (MR2798142)

45. Manish Gogna, Rakesh Kumar∗ and R. K. Nagaich, Totally umbilical CR-lightlike submanifolds of indefinite Kaehler manifolds, Bull. Math. Anal.Appl., 2 (4) (2010), 54–61. (MR2747887)

9 of 17

46. Rakesh Kumar∗, Rachna Rani and R. K. Nagaich, Some properties oflightlike submanifolds of semi-Riemannian manifolds, Demonstratio Math.,43 (3) (2010), 691–701. (ESCI & SCOPUS Indexed) (MR2683366)

47. Rakesh Kumar∗, Rachna Rani and R. K. Nagaich, The axiom of spheresin semi-Riemannian geometry with lightlike submanifolds, Kodai Math. J.,32 (2009), 52–58. (SCI & SCOPUS Indexed) (MR2518553)

48. Rachna Rani, Rakesh Kumar∗ and R. K. Nagaich, Constancy of φ sectionalcurvatures of (ε)-Sasakian manifold, Lobachevskii J. Math., 30 (1) (2009),76–80. (SCOPUS Indexed) (MR2506057)

49. Rakesh Kumar∗, Rachna Rani and R. K. Nagaich, Constancy of φ-holomo-rphic sectional curvature in indefinite Sasakian manifolds, Int. Elec.J. Geom., 2 (1) (2009), 34–40. (MR2501384)

50. Rakesh Kumar∗ and R. K. Nagaich, Indefinite RK-manifolds of constantholomorphic sectional curvature, Int. J. Math. Anal., 3 (11) (2009), 527–534. (SCOPUS Indexed) (MR2553966)

51. Jasleen Kaur, Rakesh Kumar∗, S. B. Singh and R. K. Nagaich, A noteon indefinite Quasi-Kaehler manifolds with constant holomorphic sectionalcurvature, Int. J. Math. Anal., 3 (24), (2009), 1177–1182. (SCOPUSIndexed) (MR2604357)

52. Rakesh Kumar∗ and R. K. Nagaich, Generlaziation of Cartans Lemma forindefinite K-spaces, Lobachevskii J. Math., 29 (1) (2008), 21–23. (SCOPUSIndexed) (MR2411207)

53. Rakesh Kumar∗, Jasleen Kaur and R. K. Nagaich, Indefinite Quasi Kahlermanifolds, Bull. Cal. Math. Soc., 100 (2) (2008), 177-184. (MR2437542)

54. Rakesh Kumar∗, Rachna Rani and R. K. Nagaich, On sectional curvaturesof (ε)-Sasakian manifolds, Int. J. Math. Math. Sci., Volume (2007), ArticleID 93562, 1–8. (SCOPUS Indexed) (MR2365734)

55. R. K. Nagaich and Rakesh Kumar∗, Conditions of constancy of holomorp-hic sectional curvature in an K-space, Ganita, 58 (1) (2007), 41–46. (MR25-26003)

56. Rakesh Kumar∗ and R. K. Nagaich, The axiom of Coholomorphic 3-spheres in an indefinite K-space, Bull. Cal. Math. Soc., 97 (4) (2005),373–376. (MR2189605)

Book/ChapterPublications 1. A book entitled The Geometry of Slant Lightlike Submanifolds

jointly written with Dr Rashmi Sachdeva and Dr S. S. Bhatia has beenpublished by Scholar’s Press, International Book Market Service Limited,Mauritius on February, 2018 with ISBN 978-620-2-30702-4.

10 of 17

2. A book entitled Manifolds with Indefinite Metrics jointly written byJasleen Kaur, Rakesh Kumar and R. K. Nagaich has been published byLAP Lambert Academic Publishing, Germany on November 11th, 2014with ISBN-13: 978-3-659-63256-3 and ISBN-10: 3659632562.

3. Edited and Compiled the Abstract Book of International Conferenceon EmergingAreas of Mathematics for Science and Technologyin conjunction with the 12th Annual Conference of the Indian Societyof Industrial and Applied Mathematics, organized by the Department ofMathematics, Punjabi University, Patiala, from January 30 to February 1,2015.

4. Published a chapter Generic Lightlike Submanifolds of IndefiniteKaehler Manifolds, with page no. 22-33 in a book entitled DifferentialGeometry, Functional Analysis and Applications, published by the NarosaPublishing House Pvt. Ltd. ISBN 978-81-8487-421-1.

5. Published a chapter Slant Lightlike Submanifolds of Indefinite almostContact Manifolds, with page no. 46-56 in a book entitled DifferentialGeometry, Functional Analysis and Applications, published by the NarosaPublishing House Pvt. Ltd. ISBN 978-81-8487-421-1.

CountryVisted • Italy (To attend School and workshop at ICTP in 2015)

• Poland (To deliver an invited talk in a conference in 2017)

• Germany

Citations asper GoogleScholar

• Citations: 110

• h-index: 05

• i10-index: 01

ConferenceOrganized 1. International Conference on Emerging Areas of Mathematics for

Science & Technology in conjunction with the 12th Annual Conferenceof the Indian Society of Industrial and Applied Mathematics, from 30thJanuary to 1st February, 2015.

PaperPresentations 1. Presented a paper in International Conference on Differential Geo-

metry, Algebra and Analysis organized by Department of Mathematics,Jamia Milia Islamia, New Delhi, during November 15–17, 2016.

11 of 17

2. Presented a paper in 18th International Conference of InternationalAcademy of Physical Sciences (CONIAPS-XVIII) on the RecentTrends in Physical Sciences, organized by Faculty of Sciences, Universityof Allahabad, Allahabad, during December 22–24, 2015.

3. Presented a paper in National Conference on Recent Developmentin Mathematical Modelling and Fuzziology organized by Departmentof Applied Sciences, Chandigarh University, Khrar, during October 28–29,2015.

4. Presented a paper in the National Conference on Recent Trends inMathematical Sciences organized by School of Mathematics, Shri MataVaishno Devi University, Katra, Jammu & Kashmir, during October 8–9,2015.

5. Presented a paper in International Conference on Recent Trendsin Mathematics organized by Department of Mathematics, University ofAllahabad, Allahabad during July 10–12, 2015.

6. Presented a paper in International Conference on Emerging Areasof Mathematics for Science & Technology organized by Departmentof Mathematics, Punjabi University, Patiala during 30th January to 1stFebruary, 2015.

7. Presented a paper in National Conference on Differential Geometry& its Applications organized by Department of Mathematics, Universityof Allahabad, Allahabad, during December 27–28, 2014.

8. Presented a paper in the International Conference on Algebra, Geo-metry, Analysis and Their Applications organized by Department ofMathematics, Jamia Milia Islamia, New Delhi, during November 27–29,2014.

9. Presented a paper in Conference on Exploring Basic and AppliedSciences, organized by Lovely Professional University, Jalandhar, duringNovember 14–15, 2014.

10. Presented a paper in the International Conference on DifferentialGeometry and its Applications, organized by the Department of Mathe-matics, Jadavpur University, Kolkata in collaboration with The TensorSociety, during October 16–18, 2014.

11. Presented a paper in the International Conference on MathematicalModeling and Statistical Analysis organized by PG Department ofMathematics, JC DAV College, Dasuya, Hoshiarpur, on September 30,2014.

12. Presented a paper in International Conference on Advances in Pureand Applied Mathematics, organized by Department of Mathematics,Government Degree College, Haripur (Manali), Himachal Pradesh, duringMarch 7–9, 2014.

12 of 17

13. Presented a paper in International Conference on Differential Ge-ometry and Relativity 2013, organized by Department of Mathematics,Deen Dyal Upadhyaya Gorakhpur University, Gorakhpur in collaborationwith The Tensor Society, during November 09–11, 2013.

14. Presented a paper in the International Conference on Informationand Mathematical Sciences, organized by Department of Mathematics,Baba Farid College of Engineering and Technology, Bathinda, Punjab,during October 24–26, 2013.

15. Presented a paper in the International Conference in MathematicalSciences, organized by Department of Mathematics, Government DegreeCollege, Haripur (Manali), Himachal Pradesh, during March 8–9, 2013.

16. Presented a paper in the International Conference on DifferentialGeometry and Relativity, organized by Department of Mathematics,Aligarh Muslim University, Aligarh in collaboration with The Tensor Society,during November 20–22, 2012.

17. Presented a paper in the International Conference on DifferentialGeometry, Functional Analysis and Applications, organized by theDepartment of Mathematics, Jamia Millia Islamia, New Delhi during Sept.08–10, 2012.

18. Presented a paper in the National Conference on Recent trends inMathematics and Its Applications, organized by the Department ofMathematics, Sant Longowal Institute of Engineering and Technology, Lon-gowal, Distt Sangrur, during December 16–17, 2011.

19. Presented a paper in the 2nd International Conference on RecentAdvancement in Technology and Management, organized by theContinental Group of Institutes, Jalvehra, Fathegarh Sahib on November5, 2011.

20. Presented a paper in 13th International Conference of InternationalAcademy of Physical Sciences (CONIAPS-XIII) on the EmergingInterfaces of Physical Sciences and Technology, organized by theUniversity of Petroleum and Energy Studies, Dehradun, Uttarakhand duringJune 14–16, 2011.

21. Presented a paper in 14th Punjab Science Congress, Theme: Role ofScientific Innovations and Knowledge in Economic Development,organized by the Sant Longowal Institute of Engineering and Technology,Longowal during February 7–9, 2011.

22. Presented a paper in International Conference on Recent Trendsin Mathematics and its Applications, organized by Department ofMathematics, Jamia Millia Islamia, New Delhi during March 30–31, 2009.

23. Presented a paper in 8th Punjab Science Congress, organized by theDepartment of Zoology, Punjabi University, Patiala, during February 7–9,2005.

13 of 17

Conference/WorkshopsAttended

1. Attended a Short Term Course for Assistant Professor Grade III on QualityManagement in Higher Education organized by the Human ResourceDevelopment Centre, Panjab University, Chandigarh, during January 17-23, 2017.

2. Attended School and Workshop on Complex Analysis, Geometryand Dynamics, organized by The Abdus Salam International Centre forTheoretical Physics (ICTP), Trieste, Italy from 21st September to 3rdOctober, 2015.

3. Attended 30th Annual Conference of Ramanujan MathematicalSociety organized by Indian Institute of Science Education and Research,Mohali during May 15–17, 2015.

4. Attended one day workshop on Some High Points of UndergraduateMathematics Education organized by Ramanujan Mathematical Societyat Indian Institute of Science Education and Research, Mohali on May 14th,2015.

5. Attended ATM workshop on Lattices: Geometry and Dynamicsorganized by Indian Institute of Science Education and Research, Mohaliin collaboration with National Center for Mathematics, during December17–22, 2014.

6. Attended NRC-M Workshop on Phase-field Modelling organised byUGC Networking Resource Centre for Materials, Department of MaterialsEngineering, Indian Institute of Science, Bangalore during June 08–12,2014.

7. Attended Teacher Enrichment Workshop (TEW) on Finite GroupTheory, organized by Department of Mathematics, Punjabi University,Patiala in collaboration with National Centre of Mathematics during May27 to June 2, 2014.

8. Attended Instructional School for Lecturers on Topology and Geo-metry organized by Harish Chandra Research Institute, Jhunsi, Allahabadin collaboration with the National Centre for Mathematics and AdvancedTraining in Mathematics, during December 16–28, 2013.

9. Attended one day technical workshop on the Smart Technologies inEducation organized by the Academic Staff College, Punjabi University,Patiala on January 15, 2013.

10. Attended 15th Punjab Science Congress, organized by Guru NanakDev University, Amritsar during February 7–9, 2012.

11. Attended a Workshop on Differential Geometry, organized by theDST Centre for Interdisciplinary Mathematical Sciences, Banaras HinduUniversity, Varanasi, during May 02–11, 2011.

12. Attended International Congress of Mathematicians (ICM-2010)at Hyderabad during 19–27 August, 2010.

14 of 17

13. Attended UGC Sponsored Refresher Course organized by AcademicStaff College, Punjabi University, Patiala during May 03–22, 2010.

14. Attended UGC Sponsored Workshop on Emerging Technologies inNano Sciences, organized by Department of Physics, Punjabi University,Patiala on February 20, 2008.

15. Attended UGC Sponsored Orientation Program, organized by theAcademic Staff College, Aligarh Muslim University, Aligarh during 17thMay to 13th June, 2006.

16. Attended UGC Sponsored Refresher Course, organized by the UGCRefresher Course Centre, Thapar Institute of Engineering & Technology,Patiala during December 12–31, 2005.

Papersreviewed forMathematicalReviews

1. D.H. Jin, Generic lightlike submanifolds of an indefinite Kaehler manifoldwith a non-metric φ-symmetric connection, Commun. Korean Math.Soc., 32(4) (2017), 1047–1065.

2. Andreea Olteanu, Doubly Warped Products in Locally Conformal AlmostCosymplectic Manifolds, Int. Electron. J. Geom., 10(2) (2017), 73–81.

3. Yoon-Tae Jung, A-Ryong Kim, and Soo-Young Lee, The existence and thecompleteness of some metrics on Lorentzian warped product manifolds withfiber manifold of class (B), Honam Mathematical J., 39(2) (2017), 187–197.

4. Li u, Juan Zhang, Xun Xie, Hypersurfaces satisfying τ2(φ) = ητ(φ) inpseudo-Riemannian space forms, Math. Phys. Anal. Geom., 20 (2017),1–23.

5. Hyang Sook Kim and Jin Suk Pak, Integral curves of the characteristicvector fields on CR-submanifolds of maximal CR-dimension, Commun.Korean Math. Soc., 32 (1) (2017), 107–118.

6. F. Massamba and S. Ssekajja, A note on quasi-generalized CR-lightlikegeometry in the indefinite nearly µ-Sasakian manifolds, Int. J. Geom.Methods Mod. Phys., 14 (3) (2017), 1–17.

7. Miroslava Antic, Four dmensional CR submanifolds of the sphere S6(1)with two dimensional nullity distribution, J. Math. Anal. Appl., 445(2017), 1–12.

8. Hakan Mete Tastan and Mukut Mani Tripathi, Semi-slant submanifolds ofa locally conformal Kahler manifold, An. Stiint. Univ. Al. I. CuzaIassi Mat. (N.S.), 62 (2016), 337–347.

9. S.S. Shukla and Akhilesh Yadav, Pseudo-slant lightlike submanifolds ofindefinite Sasakian manifolds, An. Stiint. Univ. Al. I. Cuza IassiMat. (N.S.), 62 (2016), 571–583.

15 of 17

10. Adela Mihai and Ion Mihai, CR-Submanifolds in Complex and SasakianSpace Forms, Chapter 8, Geometry of Cauchy-Riemann Submanifolds,217-266, Springer, Singapore (2016).

11. Velichka Milousheva and Nurettin Cenk Turgay, Quasi-minimal Lorentzsurfaces with pointwise 1-type Gauss map in pseudo-Euclidean 4-space, J.Geom. Phys., 106 (2016), 171–183.

12. Akram Ali, Wan Ainun Mior Othman, Cena Ozel, Characterizations ofcontact CR-warped product submanifolds of nearly Sasakian manifolds,Balkan J. Geom. Appl., 21 (2) (2016), 9–20.

13. Marie-Amelie Lawna and Miguel Ortega, A fundamental theorem for thehypersurfaces in semi-Riemannian warped products, J. Geom. Phys., 90(2015), 55–70.

14. Yoon-Tae Jung, Jeong-Mi Lee and Ga-Young Lee, The completeness ofsome metrics on Lorentzian warped product manifolds with fiber manifoldof Class (B), Honam Mathematical J., 37 (1) (2015), 127–134.

15. H. Mirandola and F. Vitorio, Global isometric embeddings of multiplewarped product metrics into quadrics, Kodai Math. J., 38 (2015), 119–134.

16. Shuhei Oshio and Yoshio Matsuyama, On hypersurfaces in a real spaceform with the Ricci tensor satisfying certain conditions, The InternationalConference Differential Geometry - Dynamical Systems. DGDS-2014, September 1-4, 2014, 61–68.

17. Mohammed Jamali, Jae-Bok Jun, Mohammad Hasan Shahid and MobinAhmad, A remark on the axiom of spheres with lightlike submanifolds andapplication of Jacobi equation, Bull. Malays. Math. Sci. Soc., 37 (2)(2014), 565–574.

18. Jorge H. ira and Gabriela A. Wanderley, Existence of Nonparametric Solutionsfor a Capillary Problem in Warped Products, Pacific J. Math., 269 (2)(2014), 407–424.

19. S. Kazan and B. Sahin, Pseudosymmetric lightlike hypersurfaces, Turk.J. Math., 38 (2014), 1050–1070.

20. D. H. Jin, Geometry of lightlike submanifolds of an indefinite Kenmotsumanifold, Honam Mathematical J., 36 (4) (2014), 707–722.

21. Shyuichi Izumiya, Takami Sato, Lightlike hypersurfaces along spacelikesubmanifolds in Minkowski spacetime, J. Geom. Phys., 71 (2013), 30–52.

22. D. H. Jin, Eintein half lightlike submanifolds of a Lorentzian space formwith a semi-symmetric non-metric connection, J. Inequal. Appl., 2013;403.

23. D. H. Jin, Two characterization theorems for lightlike hypersurfaces of asemi-Riemannian space form, Honam Mathematical J., 35 (3) (2013),329–342.

16 of 17

24. Suleyman Cengiz,Lightlike hypersurfaces with harmonic curvature in theLorentzian space form, Bull. Math. Anal. Appl., 5 (4) (2013), 14-18.

25. Brian Carlsen and Jeanne N. Clelland, The geometry of lightlike surfacesin Minkowski space, J. Geom. Phys., 74 (2013), 43–55.

Dr. Rakesh Kumar

17 of 17