Author
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
More filters
02 Dec 2016
TL;DR: In this article, a necessary and sufficient condition for a φ -pseudo symmetric LP-Sasakian manifold with respect to a quarter symmetric non-metric connection was obtained.
Abstract: The object of the present paper is to study φ -pseudo symmetric and φ -pseudo Ricci symmetric LP-Sasakian manifolds with respect to Levi–Civita connections and quarter-symmetric non-metric connections. We obtain a necessary and sufficient condition for a φ -pseudo symmetric LP-Sasakian manifold with respect to a quarter symmetric non-metric connection to be φ -pseudo symmetric LP-Sasakian manifold with respect to a Levi–Civita connection.
2 citations
TL;DR: In this article, a set of geometric and physical properties of hyper-generalized quasi-Einstein spacetime are discussed, including pseudosymmetry over a hypergeneralized version of spacetime.
Abstract: In this paper, we discuss about a set of geometric and physical properties of hyper-generalized quasi-Einstein spacetime. In the beginning, we discuss about pseudosymmetry over a hyper-generalized ...
1 citations
TL;DR: In this article, the authors have studied the properties of indefinite η-Einstein Sasakian manifold and introduced an example of a SISKIAN manifold with an example.
Abstract: This present paper is to study on indefinite η-Einstein Sasakian manifold which is introduced with an example. Here some properties of indefinite η-Einstein Sasakian manifold have been studied.
1 citations
01 Mar 2018
TL;DR: In this article, the authors studied characterizations of odd and even dimensional pseudo generalized quasi Einstein manifold and gave three and four dimensional examples (both Riemannian and Lorentzian) to show the existence of such manifold.
Abstract: In this paper we study characterizations of odd and even dimensional pseudo generalized quasi Einstein manifold and we give three and four dimensional examples (both Riemannian and Lorentzian) of pseudo generalized quasi Einstein manifold to show the existence of such manifold. Also in the last section we give the examples of warped product on pseudo generalized quasi Einstein manifold.
1 citations
TL;DR: In this article, the authors studied characterizations of odd and even dimensional mixed super quasi-Einstein manifold and gave three and four dimensional examples (both Riemannian and Lorentzian) of such manifold.
Abstract: Abstract In this paper we study characterizations of odd and even dimensional mixed super quasi- Einstein manifold and we give three and four dimensional examples (both Riemannian and Lorentzian) of mixed super quasi-Einstein manifold to show the existence of such manifold. Also in the last section we give the examples of warped product on mixed super quasi-Einstein manifold.
1 citations
Cited by
More filters
Journal Article•
511 citations
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
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