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.


53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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[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
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