On the existence of generalized quasi-Einstein manifolds

Uday Chand De; Sahanous Mallick

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$N (k)$ -quasi Einstein manifolds satisfying certain curvature conditions

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On generalized M-projectively recurrent manifolds

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The purpose of the present paper is to study generalized M-projectively recurrent manifolds. Some geometric properties of generalized M projectively recurrent manifolds have been studied under certain curvature conditions. An application of such a manifold in the theory of relativity has also been shown. Finally, we give an example of a generalized M-projectively recurrent manifold.

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

Sahanous Mallick, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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 $G {(Q E)}_{4}$ 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.