On quasi Ricci symmetric manifolds
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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.
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.
참고문헌 (5)
- A.L. Besse, "Einstein Manifolds" (1987), Springer
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- M.C. Chaki, "On conformally at pseudo Ricci symmetric manifolds", Tensor, N.S, 52, pp.217~222 (1993)
- F. Ozen, "On weakly and pseudo-symmetric Riemannian spaces", Indian J.pure Appl.Math, 33, pp.1477~1488 (2002)
- S. Ray-Guha, "On perfectuid pseudo Ricci symmetric space-time", Tensor, N.S, 67, pp.101~107 (2006)