On a Semi Symmetric Metric Connection With a Special Condition On a Riemannian Manifold

Hulya Yilmaz, Füsun Özen Zengin, S. Aynur Uysal

Abstract

In this study, we consider a manifold equipped with semi symmetric metric connection whose the torsion tensor satisfies a special condition. We investigate some properties of the Ricci tensor and the curvature tensor of this manifold . We obtain a necessary and sufficient condition for the mixed generalized quasi-constant curvature of this manifold. Finally, we prove that if the manifold mentioned above is conformally flat, then it is a mixed generalized quasi- Einstein manifold and we prove that if the sectional curvature of a Riemannian manifold with a semi symmetric metric connection whose the special torsion tensor is independent from orientation chosen, then this manifold is of a mixed generalized quasi constant curvature.

Keywords

Semi symmetric metric connection, Generalized quasi -Einstein manifold, Mixed generalized quasi constant curvature manifold, Mixed generalized quasi -Einstein manifold

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