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.

On partially pseudo symmetric -contact Riemannian manifolds.

Abstract: A Riemannian manifold (M, g) is semi-symmetric if (R(X,Y ) ◦ R)(U, V,W ) = 0. It is called pseudo-symmetric if R ◦ R = F, F being a given function of X, . . . ,W and g. It is called partially pseudosymmetric if this last relation is fulfilled by not all values of X, . . . ,W . Such manifolds were investigated by several mathematicians: I.Z. Szabó, S. Tanno, K. Nomizu, R. Deszcz and others. In this paper we investigate K-contact Riemannian manifolds. In these manifolds the structure vector field ξ plays a special role, and this motivates our interest in the partial pseudo-symmetry of these manifolds. We also investigate the case when R◦R is replaced by R◦S (S being the Ricci tensor). We obtain conditions in order that our manifold be: (1) Sasakian or Sasakian of constant curvature 1 (in case of R ◦ R); (2) an Einstein manifold (in case of R ◦ S). – Our investigation is closely related to the results of S. Tanno.

Certain Investigations on Pseudo Quasi-Einstein Manifolds

Abstract: Characterization of pseudo quasi-Einstein manifolds has been done in this paper. Also the existence of a pseudo quasi-Einstein manifold have been proved by several non-trivial examples. Finally some light is also thrown on conformally flat pseudo quasi-Einstein spacetimes and viscous fluid pseudo quasi-Einstein spacetimes.

$$\delta $$ δ -Almost Yamabe Solitons in Paracontact Metric Manifolds

Abstract: The goal of the current paper is to characterize paracontact metric manifolds conceding $$\delta $$ -almost Yamabe solitons. A few fascinating results of such solitons are established. Specifically, we classify $$\delta $$ -almost Yamabe solitons on $$(k,\mu )$$ and N(k)-paracontact metric manifolds.

On interpolating sesqui-harmonic Legendre curves in Sasakian space forms

Abstract: We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating se...

ON LOCALLY 𝜙-CONFORMALLY SYMMETRIC ALMOST KENMOTSU MANIFOLDS WITH NULLITY DISTRIBUTIONS

Abstract: The aim of this paper is to investigate locally φ-conformally symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.

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