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A `xi`-Projectively Flat Connection on Kenmotsu Manifolds

عنوان مقاله: A `xi`-Projectively Flat Connection on Kenmotsu Manifolds
شناسه ملی مقاله: JR_MACO-1-1_002
منتشر شده در در سال 1399
مشخصات نویسندگان مقاله:

Vahid Pirhadi - University of Kashan

خلاصه مقاله:
‎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.

کلمات کلیدی:
‎Kenmotsu manifold‎, ‎`eta`-Einstein manifold‎, ‎`xi`-concircular flat manifold‎, `xi`-conformally flat manifold‎, ‎`xi`-conharmonically flat manifold‎, ‎`xi`-projectively flat manifold‎.

صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1144614/