Quasi-conformally flat manifolds satisfying certain condition on the Ricci tensor

Abstract

The object of the present paper is to study a non-flat quasi-conformally flat Riemannian manifold whose Ricci tensor $S$ satisfies the condition $S(X,Y)=\gamma T(X)T(Y)$, where $\gamma$ is the scalar curvature and $T$ is a 1-form defined by $T(X)=g(X,\xi )$, $\xi$ is a unit vector field.