Showing papers by "Uday Chand De published in 2013"
Journal Article•
TL;DR: In this paper, the properties of hypersurfaces of a Riemannian manifold with a semi-symmetric non-metric connection were studied and the authors extended the work of Agashe and Chafle.
Abstract: Extending the work of Agashe and Chafle on semi-symmetric non-metric connection on a Riemannian manifold, we Study !he properties of hypersurfaces of a Riemannian manifold with a semi-symmetric non-metric connection
48 citations
TL;DR: In this paper, a Riccisemisymmetric 3-dimensional f-Kenmotsu manifold is studied and Ricci solitons are shown to be Ricci semi-symmetric if and only if it is an Einstein manifold.
Abstract: The aim of the present paper is to study 3-dimensional f-Kenmotsu manifolds and Ricci solitons. First, we give an example of a 3-dimensional f-Kenmotsu manifold. Then we consider a Riccisemisymmetric 3-dimensional f-Kenmotsu manifold and prove that a 3-dimensional f-Kenmotsu manifold is Ricci semisymmetric if and only if it is an Einstein manifold. Moreover, we investigate an η-parallel Ricci tensor in a 3-dimensional f-Kenmotsu manifold. Finally, we study Ricci solitons in a 3-dimensional f-Kenmotsu manifold.
30 citations
01 Jan 2013
TL;DR: In this paper, the object of the present paper is to study x -projectively flat and f -projective flat 3-dimensional normal almost contact metric manifolds, and an illustrative example is given.
Abstract: The object of the present paper is to study x -projectively flat and f -projectively flat 3-dimensional normal almost contact metric manifolds. An illustrative example is given.
17 citations
01 Jan 2013
TL;DR: In this article, a Sasakian manifold with quasi-conformal curvature tensors was studied and the object of the paper was to study the curvatures of the manifold.
Abstract: The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.
16 citations
17 Feb 2013
TL;DR: In this article, the existence of a generalized Ricci recurrent manifold has been proved by non-trivial examples and sufficient conditions for such a manifold to be a quasi-Einstein manifold have been obtained.
Abstract: In the present paper we have obtained sufficient conditions for a generalized Ricci recurrent manifold to be a quasi-Einstein manifold. The existence of a generalized Ricci recurrent manifold have been proved by non-trivial examples. The semi-Riemannian GR
n
is also studied.
12 citations
TL;DR: In this article, it was shown that the Ricci operator Q commutes with the structure tensor ϕ under certain conditions, and the operator Qϕ-ϕQ is invariant under a D-homothetic deformation.
Abstract: The object of the present paper is to study a transformation called the D-homothetic deformation of normal almost contact metric manifolds. In particular, it is shown that, in a (2n+1)-dimensional normal almost contact metric manifold, the Ricci operator Q commutes with the structure tensor ϕ under certain conditions, and the operator Qϕ – ϕQ is invariant under a D-homothetic deformation. We also discuss the invariance of η-Einstein manifolds, ϕ-sectional curvature, and the local ϕ-Ricci symmetry under the D-homothetic deformation. Finally, we prove the existence of these manifolds by a concrete example.
7 citations
03 May 2013
TL;DR: In this article, the authors studied Weyl pseudosymmetric and Ricci generalized pseudo-ymmetric generalized Sasakian-space-forms and considered the space-forms satisfying S.C = 0.
Abstract: The object of the present paper is to study Weyl pseudosymmetric and Ricci generalized pseudosymmetric generalized Sasakian-space-forms. The space-forms satisfying S.C = 0 is also considered.
5 citations
4 citations
TL;DR: In this paper, the authors studied harmonic Weyl conformal curvature tensors, conformally recurrent Ricci tensors and locally o-conformally symmetric contact metric manifolds whose characteristic vector field ξ belonging to the k-nullity distribution.
Abstract: The object of the present paper is to study harmonic Weyl conformal curvature tensor, conformally recurrent, cyclic parallel Ricci tensor and locally o-conformally symmetric contact metric manifolds whose characteristic vector field ξ belonging to the k-nullity distribution. Finally, we give an example to verify the result.
4 citations
30 Apr 2013
TL;DR: In this paper, a semi-symmetric metric connection with projective curvature ten-sor satisfies certain curvature conditions was studied. But the connection was not considered in this paper.
Abstract: The object of the present paper is to study a Kenmotsu manifold admitting a semi-symmetric metric connection whose projective curvature ten- sor satisfles certain curvature conditions.
3 citations
01 Nov 2013
TL;DR: In this paper, the authors classify an ＂LP＂-Sasakian manifold with a coefficient α satisfying certain curvature conditions and show the applications of such a manifold in general relativity and cosmology.
Abstract: The object of the present paper is to classify an ＂LP＂-Sasakian manifold with a coefficient α satisfying certain curvature conditions. Also ξ-concircularly flat and φ-concircularly flat ＂LP＂-Sasakian manifold with a coefficient α have been studied. Finally, we have shown the applications of such a manifold in general relativity and cosmology.