A ξ-PROJECTIVELY FLAT CONNECTION ON KENMOTSU MANIFOLDS

Document Type : Original Article

Author
Vahid Pirhadi
Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
10.29252/maco.1.1.2
Abstract
In this paper, we introduce a semi-symmetric non-metric connection on ηKenmotsu manifolds that changes an η-Kenmotsu manifold into an Einstein manifold. Next, we consider an especial version of this connection and show that every Kenmotsu manifold is ξ-projectively flat with respect to this connection. Also, we prove that if the Kenmotsu manifold M is a ξ-concircular flat with respect to the new connection, then M is necessarily of zero scalar curvature. Then, we review the sense of ξ-conformally flat on Kenmotsu manifolds and show that a ξ-conformally flat Kenmotsu manifold with respect to the new connection is an η-Einstein with respect to the Levi-Civita connection. Finally, we prove that there is no ξ-conharmonically flat Kenmotsu manifold with respect to this connection.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 1
June 2020
Pages 7-14