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

Article Sidebar

PDF
Published: Mar 30, 2019
Keywords:
quasi Ricci symmetric manifolds, Einstein, conformally flat, scalar curvature, recurrent, concurrent.
Mathematics Subject Classification:
3A55, 53B20.

Main Article Content

Jaeman Kim
Department of Mathematics Education, Kangwon National University, Chunchon 24341, Korea

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.


Article Details

References

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

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

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

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

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