ON DECOMPOSABLE AND WARPED PRODUCT GENERALIZED QUASI EINSTEIN MANIFOLDS

The object of the present paper is to study decomposable and warped productgeneralized quasi Einstein manifolds

Spacetimes with Pseudosymmetric Energy-momentum Tensor

The object of the present paper is to introduce spacetimes with pseudosymmetricenergy-momentum tensor. In this paper at first we consider the relation $R(X,Y)\cdot T=fQ(g,T)$, that is, the energy-momentumtensor $T$ of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetimeif the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetricand the converse is also true. Next we characterize the perfect fluid spacetimewith pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime withpseudosymmetric energy-momentum tensor

On a Class of Generalized quasi-Einstein Manifolds with Applications to Relativity

summary:Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss $G(QE)_{4}$ with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes

On a type of spacetime

The object of the present paper is to study a special type of spacetime. It is proved that in a conformally flat (W RS)4 spacetime with non-zero scalar curvature the vector field p defined by ɡ(X, p) = E(X) is irrotational and the integral curves of the vector field are geodesics. We also show that a conformally flat (W RS)4 spacetime with non-zero scalar curvature is the Robertson-Walker spacetime. Next possible local cosmological structure of such a spacetime is determined. Finally, we construct an example of a conformally flat (W RS)4 space-time with non-zero scalar curvature