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 |
|---|---|
| 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