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

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Jaeman Kim


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.

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