On pseudo m-projective ricci symmetric manifolds

The object of the present paper is to study pseudo M-projective Ricci symmetric manifolds denoted by (PMRS)_n. Several properties of (PMRS)_n are established and it is proved that if the scalar curvature is constant then (n + 1 - r) is an eigenvalue of the Ricci tensor S corresponding to the eigenvector P given by g(X,P) = A(X). In the section 3, assuming that the manifold (PMRS)_n is conformally flat, it is shown that if the M-projective Ricci tensor of this manifold is Codazzi type then this manifold becomes a quasi-Einstein manifold. In addition, it is proved that if P is a torse-forming vector field with constant energy then P must be a concircular.