Volume 1, Issue 1 (6-2020)                   MACO 2020, 1(1): 7-14 | Back to browse issues page

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Pirhadi V. A `xi`-Projectively Flat Connection on Kenmotsu Manifolds. MACO 2020; 1 (1) :7-14
URL: http://maco.lu.ac.ir/article-1-39-en.html
Abstract:   (1667 Views)
‎In this paper‎, ‎we introduce a semi-symmetric non-metric connection on `eta`-Kenmotsu manifolds that changes an `eta`-Kenmotsu manifold into an Einstein manifold‎. ‎Next‎, ‎we consider an especial version of this connection and show that every Kenmotsu manifold is `xi`-projectively flat with respect to this connection‎. ‎Also‎, ‎we prove that if the Kenmotsu manifold `M` is a `xi`-concircular flat with respect to the new connection‎, ‎then `M` is necessarily of zero scalar curvature‎. ‎Then‎, ‎we review the sense of `xi`-conformally flat on Kenmotsu manifolds and show that a `xi`-conformally flat Kenmotsu manifold with respect to the new connection is an `eta`-Einstein with respect to the Levi-Civita connection‎. ‎Finally‎, ‎we prove that there is no `xi`-conharmonically flat Kenmotsu manifold with respect to this connection‎.
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Type of Study: Research Article |
Published: 2020/06/16

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