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

Abstract

In this paper, we consider $N(k)$-quasi Einstein manifolds satisfying the curvature conditions $\overline{P}(\xi ,X)\cdot W_2=0$ and $\overline{P}(\xi ,X)·H=0$ where $\overline{P}$, $W_2$ and $H$ are the pseudo projective, $W_2$ 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.