On generalized weakly symmetric $(LCS)_{n}$-manifolds

Abstract

The object of the present paper is to study generalized weakly symmetric and weakly Ricci symmetric $(LCS)_{n}$-manifolds. Our aim is to bring out different type of curvature restrictions for which $(LCS)_{n}$-manifolds are sometimes Einstein and some other time remain $\eta $-Einstein. Finally, the existence of such manifold is ensured by a non-trivial example.