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Arindam Bhattacharyya

Bio: Arindam Bhattacharyya is an academic researcher from Jadavpur University. The author has contributed to research in topics: Sasakian manifold & Einstein manifold. The author has an hindex of 6, co-authored 69 publications receiving 209 citations.


Papers
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01 Jan 2000
TL;DR: In this paper, a Lorentzian para-Sasakian manifold with R(X,Y ) is shown to be locally isometric with a unit sphere S n (1).
Abstract: The present paper deals with Lorentzian para-Sasakian (briefly LP-Sasakian) manifolds with conformally flat and quasi conformally flat cur- vature tensor. It is shown that in both cases, the manifold is locally isometric with a unit sphere S n (1). Further it is shown that an LP-Sasakian manifold with R(X,Y ).C = 0 is locally isometric with a unit sphere S n (1).

71 citations

Journal ArticleDOI
TL;DR: In this article, a generalized Sasakian space form admits conformal Ricci soliton and quasi-Yamabe soliton, and it is shown that the potential function of a conformal gradient Ricci s soliton is constant.

25 citations

01 Jan 2007
TL;DR: In this paper, a mixed generalized quasi-Einstein manifold (MG(QE)n) was proposed and proved to be a Riemannian manifold with constant curvature.
Abstract: In this paper we extend the notion of generalized quasi-Einstein manifold and name it mixed generalized quasi-Einstein manifold(MG(QE)n). We prove the existence of such manifolds. We also introduce the notion of generalized quasi umbilical hypersurface of a Riemannian manifold and show that such a manifold is a mixed generalized quasi Einstein manifold. Finally, we obtain the relation between the manifolds with mixed gener- alized quasi constant curvature and the mixed generalized quasi-Einstein quasi conformally ∞at manifolds.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton and constructed a 3D (LCS)-manifold satisfying the results.
Abstract: The object of the present paper is to study some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS)$_n$-manifolds when the soliton becomes steady. Next we have studied some certain curvature conditions of (LCS)$_n$-manifolds admitting Yamabe solitons. Lastly we construct a 3-dimensional (LCS)$_n$-manifold satisfying the results.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the properties of a 3-dimensional kenmotsu manifold with conformal π-Einstein soliton and showed that it admits conformal soliton.
Abstract: The object of the present paper is to study some properties of Kenmotsu manifold whose metric is conformal $\eta$-Einstein soliton. We have studied certain properties of Kenmotsu manifold admitting conformal $\eta$-Einstein soliton. We have also constructed a 3-dimensional Kenmotsu manifold satisfying conformal $\eta$-Einstein soliton.

16 citations


Cited by
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Book
01 Jan 1970

329 citations

Book ChapterDOI
01 Oct 2007

131 citations

Journal ArticleDOI
22 Apr 2016-Filomat
TL;DR: In this article, the existence of Ricci solitons on a Lorentzian para-Sasakian manifold was shown to imply that (M, φ, ξ, η, 1) is an elliptic manifold.
Abstract: We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0 and S · R(ξ,X) = 0. We prove that on a Lorentzian para-Sasakian manifold (M, φ, ξ, η, 1), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M, 1) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M, 1) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.

67 citations

Journal ArticleDOI
TL;DR: The notion of quasi-Einstein spacetimes arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasiumbilical hypersurfaces.
Abstract: The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study quasi-Einstein spacetimes. Some basic geometric properties of such a spacetime are obtained. The applications of quasi-Einstein spacetimes in general relativity and cosmology are investigated. Finally, the existence of such spacetimes are ensured by several interesting examples.

52 citations