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.

Almost conformal Ricci solituons on $3$-dimensional trans-Sasakian manifold

Abstract: In this paper we have shown that if a $3$-dimensional trans-Sasakian manifold M admits conformal Ricci soliton $(g,V,\lambda )$ and if the vector field $V$ is point wise collinear with the unit vector field $\xi$, then $V$ is a constant multiple of $\xi$. Similarly we have proved that under the same condition an almost conformal Ricci soliton becomes conformal Ricci soliton. We have also shown that if a $3$-dimensional trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton, then the manifold is an Einstein manifold.

Ricci Soliton and eta-Ricci Soliton on Generalized Sasakian Space Form

Abstract: The aim of the present paper is to study Ricci soliton, eta-Ricci soliton and various types of curvature tensors on Generalized Sasakian space form. We have also studied conformal killing vector field, torse forming vector field on Generalized Sasakian space form. We have also established suitable examples of Kenmotsu manifold, Sasakian manifold and cosymplectic manifold respectively.

Totally Umbilical Hemislant Submanifolds of LP-Sasakian Manifold

Abstract: This paper is summarized as follows. In the first section we have given a brief history about slant and hemi-slant submanifold of LP-Sasakian manifold. This section is followed by some preliminaries about LP-Sasakian manifold. Finally, we have derived some interesting results on the existence of extrinsic sphere for totally umbilical hemi-slant submanifold of LP-Sasakian manifold.

Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection

Abstract: The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection.

Some Curvature Identities on Gradient Shrinking Conformal Ricci Soliton

Abstract: Abstract In this paper we have established some curvature identities for gradient shrinking conformal Ricci soliton.

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.