The object of the present paper is to study a type of Riemannian manifold called generalized quasi-Einstein manifold. The existence of a generalized quasi-Einstein manifold have been proved by non-trivial examples.
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 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.
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