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.

Some curvature identities on an almost conformal gradient shrinking RICCI soliton

Abstract: In this paper we have introduced the notion of almost conformai gradient shrinking Ricci soliton and established some curvature identities for almost conformai gradient shrinking Ricci soliton.

Some curvature properties of Lorentzian α-Sasakian manifolds

Abstract: The object of the present paper is to study the pseudo-projective φ-recurrent and generalized projective recurrent Lorentzian α-Sasakian manifolds. Here we show that pseudo-projective φ-recurrent Lorentzian α-Sasakian Manifold is an Einstein manifold and in the case of generalized projective φ- recurrent Lorentzian α-Sasakian manifold, we find a relation between the associated 1-forms A and B. We have also proved that the characteristic vector field ξ and vector field ρ associated to the 1-forms A and B are co-directional. We also study quasi-projectively flat Lorentzian α-Sasakian manifolds.

A Note on Slant and Hemislant Submanifolds of an Para Sasakian Manifold

Abstract: Connected almost contact metric manifold was classified by S.Tanno, as those automorphism group has maximum dimension.

Some types of weakly symmetric riemannian manifolds

Abstract: In this paper we study quasi-conformally flat and pseudo projec- tively flat weakly symmetric Riemannian manifolds. Here we prove a quasi- conformally flat (W S)n(n > 3) of non-zero constant scalar curvature is a manifold of hyper quasi-constant curvature and this manifold of non-vanishing scalar curvature is a quasi-Einstein manifold and manifold of quasi-constant curvature with respect to the 1-form T defined by T (X) = B(X) − D(X) 0, ∀ X. Also we obtain that a pseudo-projectively flat (W S)n(n > 3) of non-zero constant scalar curvature is a manifold of pseudo quasi-constant curvature and with non-vanishing scalar curvature is a quasi-Einstein manifold and manifold of pseudo quasi-constant curvature with respect to above 1-form T.

η-Ricci solitons on Lorentzian para-Sasakian manifolds

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.

On quasi-Einstein spacetimes

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.