On N(k)-Quasi Einstein Manifolds Admitting a Conharmonic Curvature Tensor

Rahuthanahalli Thimmegowda Naveen Kumar, Venkatesha Venkatesha

Abstract

In this paper, quasiEinstein manifolds whose characteristic vector field $\xi$ belongsto $k$-nullity distribution are called $N(k)$-quasi Einsteinmanifolds. Firstly, we have shown that a conharmonically flat quasiEinstein manifold is an $N\left(\frac{2a+b}{n-2}\right)$-quasiEinstein manifold. Later, we consider $N(k)$-quasi Einsteinmanifolds satisfying the conditions$\tilde{H}(\xi,X)\cdot\tilde{P}=0$ and$\tilde{H}(\xi,X)\cdot\tilde{Z}=0$. Moreover, we also studiedconharmonically pseudo-symmetric and conharmonically conservative$N(k)$-quasi Einstein manifolds.