IJPAM: Volume 72, No. 2 (2011)


Füsun Özen Zengın
Department of Mathematics
Faculty of Sciences and Letters
Istanbul Technical University
Maslak, 34469, Istanbul, Turkey

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.

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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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 2