N(K)-quasi-Einstein manifolds admitting Schouten tensor

Abstract

In this note, we study $\mathcal{N}(\kappa)$-quasi-Einstein (in short, $\mathcal{N}(\kappa)$-QE) manifolds admitting the Schouten tensor satisfying certain curvature conditions. At last, the existence of an $\mathcal{N}(\kappa)$-QE manifold is verified by an example.