Abstract

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

Keywords: Quasi Einstein manifold; $N(k)$-quasi Einstein manifold; projective curvature tensor; concircular curvature tensor; conformal curvature tensor; Ricci-pseudosymmetric manifold.

MSC: 53C25

Pages:  33$-$45     

Volume  66 ,  Issue  1 ,  2014