On mixed generalized quasi-Einstein manifolds

Abstract

In this paper we extend the notion of generalized quasi-Einstein manifold and name it mixed generalized quasi-Einstein manifold(MG(QE)n). We prove the existence of such manifolds. We also introduce the notion of generalized quasi umbilical hypersurface of a Riemannian manifold and show that such a manifold is a mixed generalized quasi Einstein manifold. Finally, we obtain the relation between the manifolds with mixed gener- alized quasi constant curvature and the mixed generalized quasi-Einstein quasi conformally ∞at manifolds.