Author

# Uday Chand De

Other affiliations: Yahoo!, Uludağ University, Kalyani Government Engineering College ...read more

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.

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TL;DR: The hypersurfaces of a Euclidean space have been studied and the existence of (QE)n manifolds is proved.

Abstract: In this paper we give some examples of a quasi Einstein manifold (QE)n. Next we prove the existence of (QE)n manifolds. Then we study some properties of a quasi Einstein manifold. Finally the hypersurfaces of a Euclidean space have been studied.

198 citations

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TL;DR: In this paper, the authors studied the Ricci tensor invariance of the Riemannian curvature tensor of the Kenmotsu manifold, which is derived from the almost contact Ricci manifold with some special conditions.

Abstract: The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

90 citations

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30 Jan 2007

TL;DR: In this paper, differentiable manifolds are used to construct Fibre Bundles and Linear Connections, and Riemannian Manifolds and Submanifolds.

Abstract: Preface / Some Preliminaries / Differentiable Manifolds / Exterior Algebra and Exterior Derivative / Lie Group and Lie Algebras / Fibre Bundles / Linear Connections / Riemannian Manifolds / Submanifolds / Complex Manifolds / Bibliography / Index.

77 citations

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74 citations

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TL;DR: In this paper, explicit formulae for Ricci operator, Ricci tensor and curvature tensor are obtained in a 3D trans-Sasakian manifold in cases of the manifold being η-Einstein or satisfying R (X, Y) · S = 0.

Abstract: In a 3-dimensional trans-Sasakian manifold, explicit formulae for Ricci operator, Ricci tensor and curvature tensor are obtained. In particular, expressions for Ricci tensor are obtained in a 3-dimensional trans-Sasakian manifold in cases of the manifold being η-Einstein or satisfying R (X, Y) · S = 0.

65 citations

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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

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511 citations

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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