AU - Pirhadi, Vahid TI - A `xi`-Projectively Flat Connection on Kenmotsu Manifolds PT - JOURNAL ARTICLE TA - lu-maco JN - lu-maco VO - 1 VI - 1 IP - 1 4099 - http://maco.lu.ac.ir/article-1-39-en.html 4100 - http://maco.lu.ac.ir/article-1-39-en.pdf SO - lu-maco 1 ABĀ  - ‎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. CP - IRAN IN - Department of Mathematics, Faculty of Mathematical Sciences, Kashan University, Kashan, Iran. LG - eng PB - lu-maco PG - 7 PT - Research Article YR - 2020