On a semi symmetric metric connection with a special condition on a Riemannian manifold
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KünyeYILMAZ, H.B., ZENGİN, F.Ö., UYSAL, S. A. (2011). On a semi symmetric metric connection with a special condition on a Riemannian manifold. European Journal of Pure and Applied Mathematics, 4 (2), 152-161.ss.
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.