Generalized Ricci-Recurrent Weyl Manifolds

This present paper is concerned with the study of the generalized Ricci-recurrent Weyl manifolds. First, we obtain a sufficient condition for the generalized Ricci-recurrent Weyl manifold admitting harmonic conformal curvature tensor to be a quasi-Einstein Weyl manifold. Also, we give an example of a quasi-Einstein Weyl manifold. Then, we prove that a generalized Ricci-recurrent Weyl manifold satisfying the Codazzi type of Ricci tensor is an Einstein Weyl manifold if and only if its scalar curvature is a prolonged covariant constant. Moreover, we prove that a generalized Ricci-recurrent Weyl manifold with a generalized concircularly symmetric tensor is an Einstein-Weyl manifold whose scalar curvature is prolonged covariant constant.