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
    Marmara University, Department of Mathematics
  • Fusun Ozen Zengin
    Istanbul Tecnichal University, Department of Mathematics
  • S. Aynur Uysal
    Dogus University, Department of Mathematics

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Published

2011-05-13

Issue

Section

Differential Geometry

How to Cite

On a Semi Symmetric Metric Connection With a Special Condition On a Riemannian Manifold. (2011). European Journal of Pure and Applied Mathematics, 4(2), 153-161. https://www.ejpam.com/index.php/ejpam/article/view/1048