On generalized recurrent Riemannian manifolds

Abstract

In this paper we study the two 1-forms A and B appearing in the definition of the generalized recurrency of a Riemannian manifold.It is shown that for a non-zero constant scalar curvature, A is closed iff B is closed.For a nonconstant scalar curvature the 1-forms A and B cannot be closed both, unless A is collinear with B. Also, we have found out some results on a generalized conformally recurrent Riemannian manifold.