On Ricci solitons in Kenmotsu manifolds with the semi-symmetric non-metric connection

Abstract

In this paper, we study 3-dimensional Kenmotsu manifolds with the semi-symmetric non-metric connection. We obtain some results on Ricci solitons in Kenmotsu manifolds with the semi-symmetric non-metric connection satisfying the conditions $\widetilde{C}(\xi ,X).\widetilde{S}$=0$,$ $\mathnormal{\widetilde{H}\left( \xi ,X\right) .\widetilde{S}}$\textnormal{=0 }and $\widetilde{P}(\xi ,X).\widetilde{C}$=0$,$ where $\widetilde{C}$ is the quasi-conformal curvature tensor, $\widetilde{S} $ is the Ricci tensor, $\widetilde{P}$ is the projective curvature tensor and $\widetilde{H}$ is the conharmonic curvature tensor. We also show that Ricci solitons are shrinking and expanding.