## On some classes of super quasi-Einstein manifolds.(English)Zbl 1197.53059

Summary: Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition $$\tilde{C}\cdot S=0$$ on a super quasi-Einstein manifold, where $$\tilde{C}$$ and $$S$$ denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
Full Text:

### References:

 [1] Chaki, M.C.; Maity, R.K., On quasi Einstein manifolds, Publ math debrecen, 57, 3-4, 297-306, (2000) · Zbl 0968.53030 [2] Chaki, M.C., On generalized quasi Einstein manifolds, Publ math debrecen, 58, 4, 683-691, (2001) · Zbl 1062.53035 [3] Chaki, M.C., On super quasi Einstein manifolds, Publ math debrecen, 64, 3-4, 481-488, (2004) · Zbl 1093.53045 [4] De, U.C.; Ghosh, G.C., On conformally flat special quasi Einstein manifolds, Publ math debrecen, 66, 1-2, 129-136, (2005) · Zbl 1075.53039 [5] Deszcz, R., On pseudosymmetric spaces, Bull soc math belg Sér A, 44, 1, 1-34, (1992) · Zbl 0808.53012 [6] Einstein, A., Grundzuge der relativitats theory, (2002), Springer Berlin [7] El Naschie, M.S., Gödel universe, dualities and high energy particles in E-infinity, Chaos, solitons & fractals, 25, 3, 759-764, (2005) · Zbl 1073.83531 [8] El Naschie, M.S., Is einstein’s general field equation more fundamental than quantum field theory and particle physics?, Chaos, solitons & fractals, 30, 3, 525-531, (2006) [9] Ghosh, G.C.; De, U.C.; Binh, T.Q., Certain curvature restrictions on a quasi-Einstein manifold, Publ math debrecen, 69, 1-2, 209-217, (2006) · Zbl 1121.53031 [10] Guha, S., On quasi-Einstein and generalized quasi-Einstein manifolds. nonlinear mechanics, nonlinear sciences and applications, I (niš, 2003), Facta univ ser mech automat control robot, 14, 821-842, (2003) · Zbl 1056.53033 [11] O’Neill, B., Semi-Riemannian geometry. with applications to relativity, Pure and applied mathematics, vol. 103, (1983), Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers] New York · Zbl 0531.53051 [12] Ray, D., Gödel-like cosmological solutions, J math phys, 12, 2797-2798, (1980) [13] Yano, K.; Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J differ geometry, 2, 161-184, (1968) · Zbl 0167.19802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.