On weakly Schouten symmetric manifolds

Abstract

This paper introduces and examines a new type of Riemannian manifold called a weakly Schouten symmetric manifold, referred to as \((WSS)_n\). We establish the existence of such a manifold through a concrete example. We also explore various geometric properties of \((WSS)_n\) under specific curvature conditions and proved sufficient criteria for these manifolds to be classified as Einstein manifolds. Finally, we analyze the properties of decomposable weakly Schouten symmetric manifolds.