On generalized G-recurrent manifolds

Abstract

In this paper, we define a type of Riemannian manifold called generalized G-recurrent manifold, and study the various properties of such a manifold. Among others, it is shown that if a generalized G-recurrent manifold is Einstein, then its associated 1-forms are closed and that if a generalized G-recurrent manifold with constant scalar curvature is conformally flat, then the manifold is semisymmetric. Furthermore a sufficient condition for a generalized G-recurrent manifold to be quasi Einstein is obtained.

Keywords

• generalized g-recurrent manifold
• einstein
• conformally flat
• semisymmetry
• quasi einstein