Rigidity of (m,ρ)-quasi Einstein manifolds

This paper deals with the study on (m,ρ)-quasi Einstein manifolds. First, we give some characterizations of an (m,ρ)-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 (m,ρ)-quasi Einstein manifold with a closed conformal vector field has a warped product structure of the form (Formula presented.), where I is a real interval, (M*,g*) is an (n-1) -dimensional Riemannian manifold and q is a smooth function on I. Finally, a non-trivial example of an (m,ρ) -quasi Einstein manifold verifying our results in terms of the potential function is presented.