Showing papers by "Uday Chand De published in 2010"
TL;DR: In this article, the authors studied the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor and obtained necessary and sufficient conditions for scalar curvature.
Abstract: The object of the present paper is to study the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions. Keywords: Generalized Sasakian-space-forms; projectively flat; projectively-semisymmetric; projectively symmetric; projectively recurrent; Einstein manifold; scalar curvature Quaestiones Mathematicae 33(2010), 245–252
51 citations
TL;DR: In this article, the authors studied pseudosymmetric and pseudo Ricci symmetric warped product manifolds M £F N and gave a condition on the warping function that M is a pseudo-symmetric space and N is a space of constant curvature.
Abstract: We study pseudo symmetric (brie∞y (PS)n) and pseudo Ricci symmetric (brie∞y (PRS)n) warped product manifolds M £F N. If M is (PS)n, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is (PRS)n, then we show that (i) N is Ricci symmetric and (ii) M is (PRS)n if and only if the tensor T deflned by (2.6) satisfles a certain condition.
15 citations
01 Jan 2010
TL;DR: In this article, the symmetric and skew-symmetric properties of a second order parallel tensor in a (k,µ)-contact metric manifold were studied, and the result showed that the second order tensor is symmetric.
Abstract: The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor in a (k,µ)-contact metric manifold.
8 citations
TL;DR: In this article, the authors studied locally and globally ϕ-quasiconformally symmetric (κ, μ)-contact manifolds, where ϕ is the number of contacts.
Abstract: The object of the present paper is to study locally and globally ϕ-quasiconformally symmetric (κ, μ)-contact manifolds.
6 citations
Journal Article•
TL;DR: In this article, it was shown that in a Kaehler manifold of dimension n ≥ 4, div R = 0 and div C = 0 are equivalent, where R and C denote the curvature tensors and Weyl conformal curvatures tensors, respectively.
Abstract: The object of the present paper is to prove that in a Kaehler manifold of dimension n ≥ 4, div R = 0 and div C = 0 are equivalent, where ’div’ denotes divergence and R and C denote the curvature tensor and Weyl conformal curvature tensor, respectively.