Ramesh Sharma, Professor

Education

B.S.(1974), M.S.(1976), Ph.D.(1980), Banaras Hindu University, India

Ph.D. 1986, University of Windsor, Canada

Published Books and Articles

A.  Edited Proceedings/Books: 

1.  Recent Advances in Riemannian and Lorentzian Geometries (Co-edited with K.L. Duggal), Contemporary Mathematics, Volume 337 (Proceedings of a special session of American Mathematical Society Meeting, Baltimore, 2003),  American Mathematical Society.

 2. Symmetries of Spacetimes and Riemannian Manifolds (Monograph, Co-authored with K.L. Duggal),  Kluwer Academic Publishers, Dordrecht, 1999.

 B. Papers published in Refereed Journals:

1. Certain results for K-contact and (k, )-contact manifolds, To appear in Journal Of Geometry. 

2.  Space-times through Hawking-Ellis construction with a background Riemannian metric (with V.V.  Reddy and S. Sivaramakrishnan), Classical and Quantum Gravity 24 (2007), 3339-3345.

3.  Conformal evolution of space-time solutions of Einstein’s equations (with K.L. Duggal), Communications in Applied Analysis 11 (2007), 15-22.  

4.  Almost Hermitian manifolds admitting a holomorphically planar conformal vector field (with A. Ghosh), Journal of Geometry 84 (2005), 45-54.  

 5. Conformal Killing vector fields on space-time solutions of Einstein’s equations and initial data (with K.L. Duggal), Nonlinear Analysis 63 (2005), e 447-454. 

6.  Conformal symmetries of Einstein’s field equations and initial data, Journal of Mathematical Physics 46 (2005), 042502-(1-8).

 7. Holomorphically planar conformal vector fields on almost Hermitian manifolds, Contemporary Mathematics ( American Mathematical Society) 337 (2003), 145-154. 

8.  Contact hypersurfaces of a Kaehler manifold, Journal of Geometry 78 (2003), 156-167.

9.  A class of conformally flat contact metric 3-manifolds (with F. Gouli-Andreou), Results in Mathematics 43 (2003), 114-120.

10. Characteristic surfaces in 3-dimensional Sasakian manifolds (Solicited Paper),  International Journal of Mathematical Sciences 1 (2002), 117-119.                                                 

11. Comment on the book “Symmetries of spacetimes and Riemannian manifolds” by Duggal/Sharma, and its review by M. Keyl , General Relativity and Gravitation 34 (2002), 1325-1326.

 12. Totally umbilical CMC hypersurfaces of a conformally recurrent manifold (with M.         Tarafdar), Note di Matematica 20 (2001), 89-92. 

13.  Intrinsic and extrinsic characterizations of contact metric manifolds, Geometry, Analysis and Applications, Ed. R.S. Pathak, World Scientific, Singapore, 2001, 119-127.

14. Conformally flat contact metric manifolds (with A.Ghosh and T. Koufogiorgos), Journal of Geometry 70(2001), 66-76.

15. On contact strongly pseudo-convex integrable CR manifolds (with A. Ghosh), Journal of Geometry 66 (1999), 116-122.        

 16. Addendum to: Curvature of contact manifolds, Journal of Geometry 65 (1999), 190-192. 

17.  Addendum to: Conformal motion of contact manifolds, Illinois Journal of Mathematics 42 (1998), 673-677.

18.  Some results on contact metric manifolds (with A. Ghosh), Annals of Global Analysis and Geometry 15 (1997), 497-507.

19.  Conformal motions of contact manifolds with characteristic vector field in the k-nullity distribution (with D.E. Blair), Illinois Journal of Mathematics 40 (1996), 552-563.

20. On the curvature of contact metric manifolds, Journal of Geometry 53 (1995), 179-190.

21. Notes on contact metric manifolds, Ulam Quarterly 3 (1995), 27 ff. 7 pp. (electronic).

22. Ricci curvature inheriting symmetries of semi-Riemannian manifolds (with K.L. Duggal), Contemporary Mathematics 170 (1994), 215-224.

23. Proper conformal symmetries of space-times with divergence-free Weyl conformal tensor, Journal of Mathematical Physics 34 (1993), 3582-3587.

24. Second order parallel tensors on contact manifolds II, Comptes Rendus Mathematical Reports of the Academy of Science, Canada 13 (1991), 259-264.

25. Locally symmetric and Ricci-symmetric contact metric manifolds (with T. Koufogiorgos), Annals of Global Analysis and Geometry 9 (1991), 177-181.

26. Proper special conformal Killing vectors and the quadratic theory of gravity, Journal of Mathematical Physics 32 (1991), 1854-1856.

27. Hypersurfaces in a conformally flat space with curvature collineation (with K. L. Duggal), International Journal of Mathematics and Mathematical Sciences 14 (1991), 595-604.

28. Exponential and trigonometric functions through functional equation, International Journal of Mathematical Education in Science and Technology 22 (1991), 150-152..

29. Generalization of Myers' theorem on contact manifolds (with D. E. Blair), Illinois Journal of Mathematics 34 (1990), 837-844.

30. Second order parallel tensors on contact manifolds, Algebras, Groups and Geometries 7 (1990), 145-152.

31. Conformal and curvature symmetries of contact metric manifolds, Comptes Rendus Mathematical Reports of the Academy of Science, Canada 12 (1990), 235-240.

32. A classification of 3-dimensional contact metric manifolds with Q  = Q (with D. E. Blair and T. Koufogiorgos), Kodai Mathematical Journal 13 (1990), 391-401.

33. Three-dimensional locally symmetric contact metric manifolds (with D. E. Blair), Bolletino Unione Matematica Italiana (7) 4-A (1990), 385-390.

34. Second order parallel tensors in real and complex space-forms, International Journal of Mathematics and Mathematical Sciences 12 (1989), 787-790.

35. Conformal vector fields in symmetric and conformal symmetric spaces, International Journal of Mathematics and Mathematical Sciences 12 (1989), 85-88.

36. Proper conformal symmetries of conformal symmetric space-times, Journal of Mathe­matical Physics 29 (1988), 2421-2422.

37. Mixed foliate CR-submanifolds of indefinite complex space-forms (with K. L. Duggal), Annali di Matematica Pura ed Applicata 149 (1987), 103-111.

38. Totally umbilical CR-submanifolds of semi-Riemannian Kaehler manifolds (with K. L. Duggal), International Journal of Mathematics and Mathematical Sciences 10 (1987), 551-556.

39. Totally umbilical CR-submanifolds of locally conformal Kaehler manifolds (with K. L. Duggal), Mathematical Chronicle 16 (1987), 79-83.

40. Conformal collineations and anisotropic fluids in general relativity (with K. L. Duggal), Journal of Mathematical Physics 27 (1986), 2511-2513.

41.  Lorentzian framed structures in general relativity (with K. L. Duggal), General Relativity and Gravitation 19 (1986), 71-77.

42.  Semi-symmetric connections in a semi-Riemannian manifold (with K. L. Duggal), Indian Journal of Pure and Applied Mathematics 17 (1986), 1276-1282.

43.  Characterization of an affine conformal vector field (with K. L. Duggal), Comptes Rendus Mathematical Reports of the Academy of Science, Canada 7 (1985), 201-205.

44.  Certain characteristics of the curvature tensor of an affinely connected manifold, Canadian Mathematical Bulletin 26 (1983), 355-357.

45.  On para-A-Einstein manifolds (with B. B. Sinha), Publications de l'Institut Mathematique(N.S.) 34 (1983), 211-215. 

46.  A relation between an affine Killing vector and the strain tensor of a pseudo-Riemannian manifold, Comptes Rendus Mathematical Reports of the Academy of Science, Canada 4 (1982), 305-307.

47.  On Einstein-like P-Sasakian manifolds, Matematicki Vesnik 6 (19)(34) (1982), 171-184.

48.  A quartic structure F4 = I (with B. B. Sinha), The Mathematics Student 48 (1980), 153-160.

49.  Hypersurfaces in an almost paracontact manifold (with B. B. Sinha), Matematicki Vesnik 4 (17)(32) (1980), 105-112.

50.  Infinitesimal affine normal variation of hypersurfaces in an affinely cosymplectic manifold (with B. B. Sinha), The Mathematics Student 48 (1980), 166-172.

51.  Infinitesimal variations of hypersurfaces of a Sasakian manifold (with B. B. Sinha), Progress of Mathematics 13 (1979), 23-30.

52.  Infinitesimal variations of hypersurfaces of an almost product and almost decomposable manifold (with B. B. Sinha), Indian Journal of Pure and Applied Mathematics 10 (1979), 1009-1019.

53.  On a structure f satisfying f 2 + af - I = 0 (with B. B. Sinha), Indian Journal of Pure and Applied Mathematics 9 (1978), 818-823.

54.  On a special quadratic structure on differentiable manifolds (with B. B. Sinha), Indian Journal of Pure and Applied Mathematics 9 (1978), 811-817.

Courses Taught

Courses taught at U.N.H.: 

Undergraduate:
M 115 Pre-Calculus
M 109 College Algebra
M 117 Calculus I
M 118 Calculus II
M 203 Calculus III
M 204 Differential equations
M 311 Linear Algebra
M 423 Complex Analysis
M 301 Differential Geometry
Tensors With Applications
M 338 Numerical Analysis.

Graduate:
M 632 Complex Variables 

Courses taught at Sri Satya Sai University (India):  

Undergraduate: Numerical Analysis,Complex variables, Group Theory

Graduate: Manifolds, General Relativity, Tensors, Differential Geometry. 

Courses taught at Michigan State University: Calculus I and II, Advanced Calculus. 

Other 

I am a Differential Geometer and a General Relativist.  I was a Fulbright lecturer at Sri Sathya Sai Institute Of Higher Learning (India) during July-August 2005. Currently I am involved in my ongoing work in contact geometry and in initial value problem in general relativity and conformal symmetry. 

I love teaching the traditional mathematics courses with immense enthusiasm.  I have been seeking excellence in teaching by presenting the seemingly dull mathematical notions in interesting and appealing manners.