Study of N(k)-Quasi Einstein Manifolds with Certain Curvature Restrictions

Abstract

This paper deals with the study of -quasi-Einstein manifolds under certain curvature restrictions. We construct the non-trivial physical and geometrical examples of -quasi-Einstein manifolds, which validate the existence of such manifolds. The necessary and sufficient conditions for which the conformally and quasi-conformally flat -quasi-Einstein manifolds satisfy certain curvature restrictions are derived. We also prove that the generator of the manifold is a Killing vector field and the integral curves generated by the characteristic vector field are geodesics.