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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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Journal Article
TL;DR: In this article, a generalized Ricci 2-recurrent Riemannian manifold is studied. But the object of this paper is not to study the manifold's structure. But rather to study its properties.
Abstract: The object of this paper is to study a Riemannian manifold called generalized Ricci 2-recurrent Riemannian manifold.

1 citations

Journal ArticleDOI
TL;DR: In this paper, almost pseudo-Q-symmetric manifolds A(PQS)n were studied and some geometric properties have been studied which recover some known results.
Abstract: The object of the present paper is to study almost pseudo-Q-symmetric manifolds A(PQS)n. Some geometric properties have been studied which recover some known results of pseudo Q-symmetric manifolds...

1 citations

Journal ArticleDOI
TL;DR: In this article , the authors characterized almost co-Kähler manifolds and co-kähler three-manifolds whose metrices are the gradient [formula: see text]-Einstein solitons.
Abstract: The aim of this paper is to characterize almost co-Kähler manifolds and co-Kähler three-manifolds whose metrices are the gradient [Formula: see text]-Einstein solitons. At first we prove that a proper [Formula: see text]-almost co-Kähler manifold with [Formula: see text] does not admit gradient [Formula: see text]-Einstein soliton. It is also shown that if a proper [Formula: see text]-Einstein almost co-Kähler manifold with constant coefficients admits a gradient [Formula: see text]-Einstein soliton, then either the manifold is a [Formula: see text]-almost co-Kähler manifold or the soliton is trivial. Next, we prove that in case of co-Kähler three-manifold the manifold is of constant scalar curvature. Moreover, either the manifold is flat or the gradient of the potential function is collinear with the Reeb vector field [Formula: see text]. Finally, we construct two examples to illustrate our results.

1 citations

Journal ArticleDOI
TL;DR: In this article, the authors characterize (κ, μ) contact metric manifolds whose concircular curvature tensor satisfies certain semisymmetry conditions, and verify that the result holds by a concrete example.
Abstract: The object of the present paper is to characterize (κ, μ)contact metric manifolds whose concircular curvature tensor satisfies certain semisymmetry conditions. We also verify that the result holds by a concrete example.

1 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