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


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.


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

Subject classification

3A55, 53B20.


Full Text:



A.L. Besse, Einstein Manifolds, Springer, Berlin (1987). (Google Scholar)

M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg.J.Phys. 15 (1988), 526–531. (Google Scholar)

M.C. Chaki and P. Chakrabarti, On conformally flat pseudo Ricci symmetric manifolds, Tensor, N.S. 52 (1993), 217–222. (Google Scholar)

F. Ozen and S. Altay, On weakly and pseudo-symmetric Riemannian spaces, Indian J.pure Appl.Math. 33 (2002), 1477–1488. (Google Scholar)

S. Ray-Guha, On perfect fluid pseudo Ricci symmetric space-time, Tensor, N.S. 67 (2006), 101–107. (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr