a ε-projectively flat connection on kenmotsu manifolds

In this paper, we introduce a semi-symmetric non-metric connection on ε- kenmotsu manifolds that changes an ε-kenmotsu manifold into an einstein manifold. next, we consider an especial version of this connection and show that every kenmotsu manifold is ε-projectively flat with respect to this connection. also, we prove that if the kenmotsu manifold m is a ε-concircular flat with respect to the new connection, then m is necessarily of zero scalar curvature. then, we review the sense of ε-conformally flat on kenmotsu manifolds and show that a ε-conformally flat kenmotsu manifold with respect to the new connection is an ε-einstein with respect to the levi-civita connection. finally, we prove that there is no ε-conharmonically flat kenmotsu manifold with respect to this connection.