Abstract. The object of the present paper is to study pseudo M-projective Ricci symmetric manifolds denoted by . Several properties of
are established and it is proved that if the scalar curvature is constant then is an eigenvalue of the Ricci tensor corresponding to the eigenvector given by . In the section 3, assuming that the manifold 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 is a torse-forming vector field with constant energy then must be a concircular.

Received: October 6, 2011

AMS Subject Classification: 53B05, 53B15

Key Words and Phrases: pseudo Ricci symmetric manifold, M-projective Ricci tensor, codazzi tensor, cyclic Ricci tensor, quadratic conformal Killing tensor, torse-forming vector field, concircular vector field

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