Showing papers by "Arindam Bhattacharyya published in 2016"

On Ricci flat warped products with a quarter-symmetric connection

Abstract: In this paper, we have computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of M [i.e; (1). dimM = 2, (2). dimM = 3, (3). \({dim M \geq 4}\)] and all the fibers are Ricci flat.

Multiply warped products quasi-Einstein manifolds with quarter-symmetric connection

Abstract: In this paper we study warped products and multiply warped products on quasi-Einstein manifolds with a quarter-symmetric connection. Then we apply our results to generalize Robertson-Walker spacetime with a quarter-symmetric connection.

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.

On some classes of mixed-super quasi-Einstein manifolds

Abstract: Abstract Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

On nearly quasi-Einstein warped products

Abstract: We study nearly quasi-Einstein warped product manifolds for arbitrary dimension n ≥ 3. In the last section we also give an example of warped product on nearly quasi-Einstein manifold. AMS Mathematics Subject Classification (2010): 53C25; 53B30; 53C15.

On φ-pseudo symmetric LP-Sasakian manifolds with respect to quarter-symmetric non-metric connections

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.

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.

Characterization on Mixed Generalized Quasi-Einstein Manifold

Abstract: In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold.