Showing papers by "Uday Chand De published in 2009"
TL;DR: In this article, it was shown that on a generalized Riemannian manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetricity are equivalent, and sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.
Abstract: The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.
28 citations
Journal Article•
TL;DR: In this article, it was proved that a locally φ -recurrent K-meansu manifold is the Robertson-Walker spacetime, and a concrete example of a three-dimensional K-Mean manifold is given.
Abstract: The object of this paper is to study φ -recurrent Kenmotsu manifolds. Also three-dimensional locally φ - recurrent Kenmotsu manifolds have been considered. Among others it is proved that a locally φ -recurrent Kenmotsu spacetime is the Robertson-Walker spacetime. Finally we give a concrete example of a three- dimensional Kenmotsu manifold.
27 citations
TL;DR: It is proved that in a three-dimensional normal almost contact metric manifold with α, β = constant if the Ricci tensor is η -parallel, then the manifold is locally ϕ -symmetric.
20 citations
Book•
30 Jan 2009
TL;DR: In this paper, almost complex manifolds, almost Hermite Manifolds and almost complex Hermite menifolds are combined with Para-Kahler Manifold.
Abstract: Preface / Almost Complex Manifolds / Almost Hermite Manifolds / Kahler Manifolds / Nearly Kahler Manifolds / ParaKahler Manifolds / Contact Manifolds / K-Contact Manifold / Sasakian Manifolds / Trans-Sasakian Manifolds / Paracontact Structure / LP-Sasakian Manifolds / Bibliography / Index.
20 citations
TL;DR: In this paper, the existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example.
Abstract: The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.
18 citations
TL;DR: In this paper, the existence of an almost pseudo conformally symmetric Riemannian manifold is shown by a non-trivial concrete example, which is a type of non-conformally flat Riemanian manifold.
Abstract: The object of the present paper is to study a type of non-conformally flat Riemannian manifold called almost pseudo conformally symmetric manifold. The existence of an almost pseudo conformally symmetric manifold is also shown by a non-trivial concrete example.
14 citations
TL;DR: In this article, a new type of Riemannian manifold called generalized concircularly recurrent manifold (GCR) was introduced and a necessary and sufficient condition for the constant scalar curvature of such a manifold was obtained.
Abstract: In this paper we study a new type of Riemannian manifold called generalized concircularly recurrent manifold. We obtain a necessary and sufficient condition for the constant scalar curvature of such a manifold. Next we study Ricci symmetric generalized concircularly recurrent manifold and prove that such a manifold is an Einstein manifold. Finally, we obtain a sufficient condition for a generalized concircularly recurrent manifold to be a special quasi-Einstein manifold.
9 citations
TL;DR: In this paper, the authors studied curvature restriction on LP-Sasakian manifold with acoefficient α and showed that the manifold is the product manifold of constant curvature.
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
6 citations
TL;DR: In this paper, the authors studied locally and globally o-quasiconformally symmetric Sasakian manifolds and showed that a globally OQSSA manifold is globally OqSSA.
3 citations
TL;DR: In this article, weakly symmetric spacetime has been studied and the existence of such a manifold has also been proved by a concrete example; see Section 2.2.1.
Abstract: In the present paper we study weakly symmetric spacetime. The existence of such a manifold has also been proved by a concrete example.
3 citations