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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, it was shown that a locally -recurrent (k, )-contact metric manifold is an Eigen manifold with constant curvature, and the existence of such a manifold is proved by a non-trivial example.
Abstract: In this paper we prove that a -recurrent (k, )-contact metric manifold is an -Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally -recurrent (k, )-contact metric manifold is the space of constant curvature. The existence of -recurrent (k, )-manifold is proved by a non-trivial example.

11 citations

Journal ArticleDOI
TL;DR: In this paper, the authors characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.
Abstract: In this paper, we characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.

11 citations

Journal ArticleDOI
TL;DR: In this paper, a 3D trans-Sasakian manifold with conservative curvature tensor and 3D conformally flat trans-sakian manifolds are studied.
Abstract: The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected -Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.

11 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that a 3D Riemannian manifold endowed with a semi-symmetric ρ-connection, whose metric is a Yamabe soliton, is a manifold of constant sectional curvature − 1 and the soliton is expanding with soliton constant − 6.

11 citations

Journal ArticleDOI
TL;DR: In this paper, the authors characterized Weyl semisymmetric almost Kenmotsu manifolds with characteristic vector field ξ belonging to the ( k, μ ) − nullity distribution and ( k, μ ) -nullity distribution respectively.

11 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