Rigidity of (m,ρ)-quasi Einstein manifolds

Abstract

This paper deals with the study on -quasi Einstein manifolds. First, we give some characterizations of an -quasi Einstein manifold admitting closed conformal or parallel vector field. Then, we obtain some rigidity conditions for this class of manifolds. We prove that an -quasi Einstein manifold with a closed conformal vector field has a warped product structure of the form , where I is a real interval, is an -dimensional Riemannian manifold and q is a smooth function on I. Finally, a non-trivial example of an -quasi Einstein manifold verifying our results in terms of the potential function is presented.