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.

Golden Riemannian structures on the tangent bundle with g-natural metrics

Abstract: Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

On ϕ-quasiconformally symmetric (κ,μ)-contact manifolds

Abstract: The object of the present paper is to study locally and globally ϕ-quasiconformally symmetric (κ, μ)-contact manifolds.

On weakly cyclic Z symmetric spacetimes

Abstract: The object of the present paper is to study weakly cyclic Z symmetric spacetimes At first we prove that a weakly cyclic Z symmetric spacetime is a quasi Einstein spacetime Then we study $${{(WCZS)}_{4}}$$ spacetimes satisfying the condition div $${C=0}$$ Next we consider conformally flat $${{(WCZS)}_{4}}$$ spacetimes Finally, we characterise dust fluid and viscous fluid $${{(WCZS)}_{4}}$$ spacetimes

η-Ricci Solitons on Kenmotsu 3-Manifolds

Abstract: Abstract In the present paper we study η-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider η-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study φ-Ricci symmetric η-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition R.R = Q(S, R)is considered. Finally, an example is constructed to prove the existence of a proper η-Ricci soliton on a Kenmotsu 3-manifold.

Kenmotsu manifolds satisfying the Fischer-Marsden equation

Abstract: The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies Lg(λ) = 0 on a (2n+ 1)-dimensional Kenmotsu manifold M2n+1, then either ξλ = −λ or M2n+1 is Einstein. If n = 1, M3 is locally isometric to the hyperbolic space H3(−1).

A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices

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.

Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions

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