Certain curvature properties of N(k)-quasi Einstein manifolds

Abstract

In this paper, we consider N(k)-quasi Einstein manifolds satisfying the curvature conditions P¯(ξ,X)⋅W2=0 and P¯(ξ,X)·H=0 where P¯, W2 and H are the pseudo projective, W2 and conharmonic curvature tensors respectively. We study pseudo projectively symmetric N(k)-quasi Einstein manifolds and show that there does not exist a pseudo projectively semisymmetric N(k)-quasi Einstein manifold. Also, we construct some examples to support the existence of such manifolds.