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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.)
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