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.

CERTAIN CURVATURE CONDITIONS ON AN LP-SASAKIAN MANIFOLD WITH A COEFFICIENT α

Abstract: . The object of the present paper is to study certain curva-ture restriction on an LP-Sasakian manifold with a coefficient α . Amongothers it is shown that if an LP-Sasakian manifold with a coefficient α is a manifold of constant curvature, then the manifold is the productmanifold. Also it is proved that a 3-dimensional Ricci semisymmetricLP-Sasakian manifold with a constant coefficient α is a spaceform. 1. IntroductionIn 1989, Matsumoto [6] introduced the notion of LP-Sasakian manifolds.Then Mihai and Rosca [7] introduced the same notion independently and theyobtained several results in this manifold. In a recent paper, De, Shaikh, andSengupta [3] introduced the notion of LP-Sasakian manifolds with a coefficient α which generalizes the notion of LP-Sasakian manifolds. Recently, T. Ikawaand his coauthors [4], [5] studied Sasakian manifolds with Lorentzian metricand obtained several results in this manifold. The object of the present paperis to study certain curvature restriction on an LP-Sasakian manifold with acoefficient

E-Bochner curvature tensor on N(k)-contact metric manifolds

Abstract: The object of the present paper is to study E-Bochner curvature tensor B e satisfying R:B e = 0, B e :R = 0, B e :B e = 0 and B e :S = 0 in an ndimensional N(k)-contact metric manifold.

Spacetimes with Pseudosymmetric Energy-momentum Tensor

Abstract: The object of the present paper is to introduce spacetimes with pseudosymmetricenergy-momentum tensor. In this paper at first we consider the relation \(R(X,Y)\cdot T=fQ(g,T)\), that is, the energy-momentumtensor \(T\) of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetimeif the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetricand the converse is also true. Next we characterize the perfect fluid spacetimewith pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime withpseudosymmetric energy-momentum tensor.

Almost quasi-Yamabe solitons and gradient almost quasi-yamabe solitons in paracontact geometry

Abstract: The purpose of the present paper is to investigate the almost quasi- Yamabe soliton and gradient almost quasi-Yamabe solitons under the framework of three-dimensional normal almost paracontact metr...

Concircular curvature on warped product manifolds and applications.

Abstract: This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson-Walker and standard static space-times.

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