Korean J. Math.  Vol 27, No 1 (2019)  pp.9-15
DOI: https://doi.org/10.11568/kjm.2019.27.1.9

On quasi Ricci symmetric manifolds

Jaeman Kim

Abstract


In this paper, we study a type of Riemannian manifold, namely quasi Ricci symmetric manifold. Among others, we show that the scalar curvature of a quasi Ricci symmetric manifold is constant. In addition if the manifold is Einstein, then its Ricci tensor is zero. Also we prove that if the associated vector field of a quasi Ricci symmetric manifold is either recurrent or concurrent, then its Ricci tensor is zero.

Keywords


quasi Ricci symmetric manifolds, Einstein, conformally flat, scalar curvature, recurrent, concurrent.

Subject classification

3A55, 53B20.

Sponsor(s)



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References


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