## Abstract

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.

Original language | English |
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Pages (from-to) | 249-258 |

Number of pages | 10 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 72 |

Issue number | 2 |

Publication status | Published - 2011 |

## Keywords

- Codazzi tensor
- Concircular vector field
- Cyclic Ricci tensor
- M-projective Ricci tensor
- Pseudo Ricci symmetric manifold
- Quadratic conformal Killing tensor
- Torseforming vector field