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.