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Sharma, Ramesh (full)
Ramesh
Sharma
Ph.D.
Professor
Arts & Sciences
Mathematics
203-932-7292
MAXY321
Maxcy Hall
About

    I am a Differential Geometer and General Relativist. Currently, my research focusses on (i) Riemannian Geometry of Complex and Contact Spaces, and (ii) Cosmological Models and Solutions of Einstein’s Field Equations with or without Symmetries. Aside from the core research, I am also keenly interested in the current issues in Cosmology, such as Dark Energy and Dark Matter. I have been involving senior undergraduate students in relevant Mathematical Projects.

    I was a Fulbright Lecturer at Sri Sathya Sai University (India) during 2005. I love teaching traditional mathematics courses with immense enthusiasm, and seek excellence in teaching by presenting the seemingly dull mathematical notions in interesting and appealing manners.

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    Published Books and Articles

    Edited Proceedings/Books:
      
    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.

    Symmetries of Spacetimes and Riemannian Manifolds (Monograph, Co-authored with K.L. Duggal), Kluwer Academic Publishers, Dordrecht, 1999, Springer-Verlag, NY 2009.

    Published Articles:

    Synchronous space-times with pure trace extrinsic curvature slices, Classical  and Quantum Gravity 28 (2011), 195021 (7 pp.). 

    K-contact metrics as Ricci solitons (with A. Ghosh), To appear in Beitrage zur Algebra und     Geometrie (Contributions to Algebra and Geometry). 

    An inductive proof of the condition for AM-GM Equality (with C. Barratt), To appear in     Mathematical Gazette.

    Sasakian 3-manifold as a Ricci soliton represents the Heisenberg group (with A. Ghosh), International Journal of Geometric Methods in Modern Physics 8 (2011), 149-154.

    Normal Vector As An Eigenvector Of The Weingarten Matrix (with N. Uday Kiran and M.S. Srinath), International Electronic Journal of Geometry 4 (2011), 125-128.

    A Level Set Method-Based Derivation of Differential Equation for Developable Surfaces (with  N. Uday Kiran and M.S. Srinath), International Electronic Journal of Geometry 3  (2010), 11-15.

    Contact geometry and Ricci solitons (With J.T. Cho), International Journal of Geometric  Methods in Modern Physics 7 (2010), 951-960.

    Perfect fluids whose energy-momentum tensor is conformal Killing (with A. Ghosh), Journal  of Mathematical Physics  51 (2010), 022504 (1-5). 

    Reviewing A.M.-G.M. equality by waiving positivity (with G. Brown, H. Biao and J. Wu), International Journal of Pure and Applied Mathematics 60 (2010), 229-322.

    Conformal classification of (k, )-contact manifolds (with Luc Vrancken), Kodai Mathematical  Journal 33 (2010), 267-282.

    Solutions of Einstein’s equations with conformal Killing vector fields and initial data (Invited paper, with K.L. Duggal), Nonlinear Studies 17 (2010), 37-46.

    Solutions of Einstein’s equations with conformal symmetries and a contact slice (with K.L.     Duggal), Nonlinear Analysis 71 (2009), e701-e705.

    Lorentzian metric induced from a background Riemannian metric (with V.V. Reddy and S.     Sivaramakrishnan), International Journal of Pure and Applied Mathematics 47 (2008), 343-    351.

    Contact metric manifolds with  -parallel torsion tensor (with A. Ghosh and J. T. Cho), Annals Of Global Analysis and Geometry 34 (2008), 287-299.

    Certain results for K-contact and (k, )-contact manifolds, Journal Of Geometry 89 (2008), 138-147.

    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.

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

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

    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.

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

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

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

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

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

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

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

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

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

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

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

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

    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.

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

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

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

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

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

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

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

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

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

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

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

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

    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.

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

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

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

    Proper conformal symmetries of conformal symmetric space-times, Journal of Mathe¬matical Physics 29 (1988), 2421-2422.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    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.

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

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

    Presentations at Conferences and Academic Institutions:

    Differential equations in cosmology, Symposium on Differential Equations, Sri Sathya Sai University (India), July 2011.

    Synchronous space-times with pure trace extrinsic curvature slices, Lecture delivered at Inter-University Centre for Astronomy and Astrophysics (India), July 2011.

    Our Universe: Dark energy and Dark matter, Colloquium Lecture at Sri Sathya Sai University (India), July 2011. 

    Non-trivial Ricci Solitons on 3-D Sasakian manifolds and their obstruction to compactness,Invited talk at the special session “Geometric and topological problems in curvature” of the American Mathematical Society’s meeting, College of Holy Cross (Massachusetts), April 2011.

    Sasakian 3-metric as Ricci soliton represents the Heisenberg group, ½ - hour talk at the Satellite conference at the Indian Institute Of Science, Bangalore, India, of the International Congress of  Mathematicians,  Aug. 12-15, 2010.

    Weyl curvature and spatial isotropy of synchronous space-times, 1-hour talk at the conference “Geometric and Probablistic aspects of General Relativity” at the University of Strasbourg (sponsored by CNRS, France) , June 10-12, 2010.
    Space-times admitting a quadratic conformal Killing tensor, 13th Eastern Gravity Meeting, North Carolina State University, Raleigh, May 21-22, 2010.

    AM-GM equality, Presented by co-author C. Barratt at the North-Eastern Sectional Fall     Meeting of the Mathematical Association of America, Springfield, MA, Nov. 20-21, 2009.

    Contact geometry and Ricci solitons, Invited talk at Dartmouth Geometry and Topology     seminar, Dartmouth College, Nov. 2009.

    Ricci solitons in contact geometry, Invited talk at the special session “Symplectic, contact and  complex structures” of the American Mathematical Society’s meeting, Pennsylvania State University (University Park), Oct. 2009.

    Arithmetic Mean–Geometric Mean Equality, Colloquium talk at the Department of     Mathematics, Sri Sathya Sai University, July, 2009.

    Solutions of Einstein’s equations with conformal symmetries and initial data, Invited talk at     the 14th Canadian conference on General Relativity and Relativistic Astrophysics,     South     Alberta Institute Of Technology, Calgary, Canada, May 2009.

    Means in n-dimensions: Exploring equalities of numbers through certain equations (joint with     G. Brown, H. Biao and J. Wu). Presented by G. Brown at North Eastern Sectional meeting of Mathematical Association Of America , Bentley College, Nov. 2008.

    Conformal geometry of contact metric manifolds, Invited talk at the special session             “Riemannian and Lorentzian Geometries” of the American Mathematical Society’s meeting,     Wesleyan University (Connecticut), Oct. 2008.

    Weyl conformal tensor and conformal symmetries of generalized Robertson-Walker         space-times, 1-hour Invited talk at the Raman Research Institute, Bangalore, India, Aug. 2008.

    Differential geometry and Cosmology, Colloquium talk at the Mathematics Department of Sri Sathya Sai University (India), July, 2008.
      
    Evolution of solutions of Einstein’s equations out of a contact Riemannian metric, Invited talk     at the 5th World Congress of Nonlinear Analysts, Orlando, Florida, July, 2008.

    Conformal vector fields on space-time with an initial data, Invited talk presented by K.L. 8    Duggal (co-author) at the special session “Relativity and Gravitational Theory” of the 3rd     International Conference of Applied Mathematics, Plovdiv, Bulgaria, Aug. 2006.

    A Contact conformal characterization of an odd dimensional unit sphere, Invited talk at the     special session “Geometry of Riemannian manifolds with additional structures” of the     American Mathematical Society’s meeting, Miami, April 2006.

    Conformal symmetries of Einstein’s field equations and geometric structure of the initial data, Plenary Invited lecture under the Prestigious Theoretical Physics Seminar Circuit of the S.N.   Bose National Center for Basic Sciences, Calcutta, India, Aug. 2004.

    Conformal vector fields on spacetimes and Initial data, Invited talk presented by the co-author,     K.L. Duggal at the special session “Geometric analysis in Mathematical Physics” of the 4th     World Congress of Nonlinear Analysts, Orlando, Florida, June 30-July 7, 2004.

    Conformal vector fields on Kaehler manifolds and contact hypersurfaces, Invited talk at the   special session “Recent developments in Riemannian and Lorentzian geometries” of American  Mathematical  Society meeting (Baltimore, Jan. 2003).

    Solutions of Einstein’s equations with conformal symmetries, Department Of Physics, Yale     University, Mar. 2002.

    Intrinsic and extrinsic characterizations of contact manifolds, Invited talk at  the International  conference on geometry, analysis and applications, B.H.U., India, Aug. 2000.

    Canonical contact hypersurfaces of Kaehler manifolds, 105th Annual meeting of American     Mathematical  Society,  Washington, D.C., Jan. 2000.

    Infinitesimal transformations of semi-Riemannian manifolds, Invited talk at the     Department of Pure Mathematics, University of Calcutta, India, Aug. 1998.

    Conformal symmetries of spatially compact spacetimes, 14th International conference on     General Relativity and Gravitation at Florence, Italy, Aug. 1995.

    Geometry of Contact manifolds, Invited talk at the Department of Pure Mathematics,     University of Calcutta, India, Aug. 1995.

    Curvature of contact metric manifolds, Department of Mathematics, University of Connecticut  (Storrs, March 1995).

    3+1 formalism on spacetimes and conformal symmetries, Department of Physics, Yale     University, Feb. 1995.

    Ricci curvature inheriting symmetry of semi-Riemannian spaces (with K.L. Duggal), Invited     talk at a special session of the Joint meeting of American and Canadian Mathematical     Societies, Vancouver,  August 1993.

    Proper conformal symmetries of spacetimes with divergence-free Weyl conformal tensor,       Invited talk at a special session "Differential Geometry" of American Mathematical Society at  San Antonio, Texas, January 1993.

    Spacetimes with conformal symmetries, Invited talk at the Department of Physics,         University of Connecticut,  Storrs, November 1992.

    Infinitesimal conformal transformation of Sasakian 3-manifolds, 6th Lehigh University     Geometry and Topology Conference, Bethlehem, Pennsylvania, 1991.

    Curvature properties of contact Riemannian manifolds, American Mathematical Society     Summer Research Institute, University of California, Los Angeles, 1990).

    Matter-symmetric solutions of Einstein field equations with conformal symmetry, Invited     talk at the 12th International Conference on General Relativity and Gravitation, University     of Colorado, Boulder, 1989.

    Special conformal collineations in locally symmetric spaces, 93rd Annual Meeting of the     American Mathematical Society, San Antonio, 1987.

    Applications of some CR-submanifolds to physical space-times, 92nd Annual Meeting of the     American Mathematical Society, New Orleans, 1986.

    A characterization of an affine conformal vector field, 88th Summer Meeting of the American Mathematical Society, Eugene, 1984.

    A research program in general relativity, 65th Ontario Mathematics Meeting, Queen’s University, Canada, 1983.

    On -Einstein Sasakian manifolds, Annual meeting of the Indian Mathematical Society, Bangalore University, 1981.

    Education

    1986 Ph.D., University of Windsor, Ontario, Canada.
    Dissertation: Cauchy-Riemann Submanifolds of Semi-Riemannian Manifolds with Application to Relativity and Hydrodynamics.

    1980 Ph.D., Banaras Hindu University, India.
    Dissertation: Differentiable manifolds with polynomial structures.

    1976  M.S., Banaras Hindu University, India.

    1974  B.S. (Honors), Banaras Hindu University, India.

    Awards/Honors

    • Excellence in Research/Creative Activity Award, University Of New Haven, 2008.
    • University Research Scholar Designation Award, University Of New Haven, 2008-2014.
    • University of New Haven Faculty Research Grants  (2008, 07, 05, 01, 1999, 98, 96, 94, 91).
    • Selected for Who’s Who Among America’s Teachers, 2006.
    • Fulbright Lecturing Grant ( India),  2005.
    • Yale University Visiting Faculty Fellowship (Yale University), 1994-95.
    • Nominated for Distinguished Teaching Award at the University of New Haven, 1993, 1995.
    • A Travel Fellowship of Connecticut Space Grant College Consortium (NASA) (1992).
    • B.H.U. Prize for standing First in B.Sc. (Mathematics Honors), India (1974).