Abstract
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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