Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ON QUASI RICCI SYMMETRIC MANIFOLDS

  • Kim, Jaeman (Department of Mathematics Education Kangwon National University)
  • Received : 2018.09.21
  • Accepted : 2018.12.18
  • Published : 2019.03.30
Download PDF
⟨ Previous Next ⟩

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

References

  1. A.L. Besse, Einstein Manifolds, Springer, Berlin (1987).
  2. M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg.J.Phys. 15 (1988), 526-531.
  3. M.C. Chaki and P. Chakrabarti, On conformally at pseudo Ricci symmetric manifolds, Tensor, N.S. 52 (1993), 217-222.
  4. F. Ozen and S. Altay, On weakly and pseudo-symmetric Riemannian spaces, Indian J.pure Appl.Math. 33 (2002), 1477-1488.
  5. S. Ray-Guha, On perfect fluid pseudo Ricci symmetric space-time, Tensor, N.S. 67 (2006), 101-107.