On Quasi-Einstein Manifolds Admitting Space-Matter Tensor

Abstract

The subject matter of this paper lies in the interesting domain of Differential Geometry and the Theory of General Relativity. Although the space has its motivation in Relativity, we study the geometric properties of the space, inspired by the papers on the geometry related to curvature restrictions. Such a study was joined by A. Z. Petrov to Einstein spaces. We extend the study on quasi-Einstein spaces which can be considered as a generalization of Einstein spaces. This study is supported by an example.

Keywords

• Space-matter tensor,Einstein's field equation,scalar curvature,Quasi-Einstein Manifolds

Kaynakça

1. [1] M. C. Chaki, R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306.
2. [2] F. Defever, R. Deszcz, M. Hotlos, M. Kucharski, Z. Senturk, Generalisations of Robertson-Walker spaces, Annales Univ. Sci. Budapest. Eotvos Sect. Math., 43 (2000), 13-24.
3. [3] R. Deszcz, M. Hotlos, On some pseudosymmetry type curvature condition, Tsukuba J. Math., 27 (2003), 13-30.
4. [4] R. Deszcz, M. Hotlos, Z. Senturk, Quasi-Einstein hypersurfaces in semi-Riemannian space forms, Colloq. Math., 81 (2001), 81-97.
5. [5] R. Deszcz, M. Hotlos, Z. Senturk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math., 27(4) (2001), 375-389.
6. [6] R. DESZCZ, VERHEYEN, P. and VERSTRAELEN, L.: On some generalized Einstein metric conditions, Publ. Inst. Math. (Beograd), 60:74 (1996), pp. 108-120.
7. [7] S. K. Jana, A. K. Debnath, J. Sengupta: On Riemannian manifolds satisfying certain curvature conditions, Bulletin of Natural and Mathematical Sciences, Russia, 30(2) (2013), 40-61.
8. [8] A. Z. Petrov, Einstein Spaces, Pergamon Press, Oxford, 1949.

9. [9] L. Tamassy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Rimannian manifolds, Coll. Math. Soc., J. Bolyai 50 (1989), 663-670 .