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Uday Chand De

Bio: Uday Chand De is an academic researcher from University of Calcutta. The author has contributed to research in topics: Ricci curvature & Riemann curvature tensor. The author has an hindex of 24, co-authored 225 publications receiving 2257 citations. Previous affiliations of Uday Chand De include Yahoo! & Uludağ University.


Papers
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TL;DR: In this article, the authors studied the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor and obtained necessary and sufficient conditions for scalar curvature.
Abstract: The object of the present paper is to study the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; projectively-semisymmetric; projectively symmetric; projectively recurrent; Einstein manifold; scalar curvature Quaestiones Mathematicae 33(2010), 245–252

51 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a generalized Robertson-Walker space-time.
Abstract: A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matter perfect fluid space-time or a mass-less scalar field with time-like gradient and with divergence-free Weyl tensor are GRW space-times.

50 citations

Journal Article
TL;DR: In this paper, the properties of hypersurfaces of a Riemannian manifold with a semi-symmetric non-metric connection were studied and the authors extended the work of Agashe and Chafle.
Abstract: Extending the work of Agashe and Chafle on semi-symmetric non-metric connection on a Riemannian manifold, we Study !he properties of hypersurfaces of a Riemannian manifold with a semi-symmetric non-metric connection

48 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied Yamabe solitons on almost co-Kahler manifolds as well as on -almost co-kahler manifold and showed that they can be solved on both of them.
Abstract: The object of this paper is to study Yamabe solitons on almost co-Kahler manifolds as well as on -almost co-Kahler manifolds.

39 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied some properties of a quasi-Einstein manifold, and a non-trivial concrete example of such a manifold is also given, where the properties of the manifold are investigated.
Abstract: The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.

36 citations


Cited by
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Journal ArticleDOI
TL;DR: This paper introduces metric-based means for the space of positive-definite matrices and discusses some invariance properties of the Riemannian mean, and uses differential geometric tools to give a characterization of this mean.
Abstract: In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization of this mean.

700 citations

Book
01 Jan 1970

329 citations

Book
04 Oct 2009
TL;DR: Holm as mentioned in this paper provides a unified viewpoint of Lagrangian and Hamiltonian mechanics in the coordinate-free language of differential geometry in the spirit of the Marsden-Ratiu school.
Abstract: ,by Darryl D. Holm, Tanya Schmah and Cristina Stoica, Oxford University Press,Oxford, 2009, xi + 515 pp., ISBN: 978-0-19-921290-3The purpose of the book is to provide the unifying viewpoint of Lagrangian andHamiltonian mechanics in the coordinate-free language of differential geometryin the spirit of the Marsden-Ratiu school. The book is similar in content - althoughless formal - to the book by J. Marsden and T. Ratiu [7]. One can also mentionthe companion two-volumes book by Holm [4,5] written at a more basic level,and that one can recommend as an introductory reading. The classical treatises onthe subject are the books by Abraham-Marsden [1], Arnold [2] and Libermann-Marle [6].Typical applications are N-particle systems, rigid bodies, continua such as u-ids and electromagnetic systems that illustrate the powerfulness of the adoptedpoint of view. The geometrical structure allows the covering of both the nite-dimensional conservative case (rst part of the book) and the innite dimensionalsituation in the second part. The notion of symmetry here is central, as it allowsa reduction of the number of dimensions of the mechanical systems, and furtherexploits the conserved quantities (momentum map) associated to symmetry. Liegroup symmetries, Poisson reduction and momentum maps are rst discussed.The concepts are introduced in a progressive and clear manner in the rst part ofthe book. The second part devoted to innite dimensional systems is motivatedby the identication of Euler’s ideal uid motion with the geodesic o w on thegroup of volume-preserving diffeomorphism. The Euler-PoincarO (EP) variationalprinciple for the Euler uid equations is exposed in the framework of geometricmechanics, in association with Lie-Poisson Hamiltonian structure of Noether’stheorem and momentum maps. Original applications of the Euler-PoincarO equa-tions to solitons, computational anatomy, image matching, or geophysical uiddynamics are given at the end of the second part of the book.Here the rst chapter recapitulates the Newtonian, Lagrangian and Hamiltonian117

254 citations