On the Non-existence of Certain Types of Weakly Symmetric Manifold

An expression for the curvature tensor of a weakly symmetric manifold is obtained. Next it is shown that an Einstein weakly symmetric manifold of dimension $>2$ does not exist. Further it is proved that a conformally flat weakly symmetric manifold of dimension $>3$ is a quasi Einstein manifold. Finally a couple of results on conformally flat weakly symmetric manifold are presented. 2000 Mathematics Subject Classification. 53B35, 53B05