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

Authors

  • Hulya Yilmaz
  • Fusun Ozen Zengin
  • S. Aynur Uysal

Keywords:

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

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.

Author Biographies

Hulya Yilmaz

Fusun Ozen Zengin

S. Aynur Uysal

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How to Cite

Yilmaz, H., Ozen Zengin, F., & 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), 153–161. Retrieved from https://ejpam.com/index.php/ejpam/article/view/1048