$N(k)$-quasi Einstein manifolds satisfying certain curvature conditions

Abstract

The object of the present paper is to study$N(k)$-quasi Einstein manifolds. Existence of $N(k)$-quasiEinstein manifolds are proved by two non-trivial examples. Also aphysical example of an $N(k)$-quasi-Einstein manifold is given. Westudy an $N(k)$-quasi-Einstein manifold satisfying the curvatureconditions $\tilde Z(\xi ,X)\cdot S=0$, $P(\xi ,X)\cdot\tildeZ=0$, $\tilde Z(\xi,X)\cdot P=0$, $\tilde Z(\xi,X)\cdot C=0$ and$P(\xi,X)\cdot C=0$. Finally, we study Ricci-pseudosymmetric$N(k)$-quasi-Einstein manifolds.