Weakly symmetric and weakly riccisymmetric conditions on manifolds

Mehmet ATÃ‡EKEN; Ãœmit YILDIRIM

doi:10.5897/AJMCSR2013.0486

African Journal of
Mathematics and Computer Science Research

Abbreviation: Afr. J. Math. Comput. Sci. Res.
Language: English
ISSN: 2006-9731
DOI: 10.5897/AJMCSR
Start Year: 2008
Published Articles: 261

Full Length Research Paper

Weakly symmetric and weakly ricciâ€“symmetric conditions on manifolds

Mehmet ATÃ‡EKEN

Mehmet ATÃ‡EKEN
Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpasa University, 60100, Tokat-Turkey
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Ãœmit YILDIRIM

Ãœmit YILDIRIM
Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpasa University, 60100, Tokat-Turkey
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Article Number - 756D6548258
Vol.6(6), pp. 130-135 , June 2013
https://doi.org/10.5897/AJMCSR2013.0486

Accepted: 26 June 2013
Published: 30 June 2013

Copyright © 2024 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0.

Abstract

In this paper, we have researched the necessary and sufficient conditions for a manifold to be weakly symmetric and weakly Ricci–symmetric and examined the conditions over 1–forms involved in the definitions of weakly symmetric and weakly Ricci–symmetric conditions. We have evaluated some certain results of situations in which a weakly symmetric manifold is with parallel or cyclic Ricci tensor. Finally, an example is used to demonstrate that the method presented in this paper is effective.