Some results on β-kenmotsu manifolds with a non-symmetric non-metric connection

Abstract

The object of the present paper is to study some results on a $\beta$-Kenmotsu manifold with a non-symmetric non-metric connection. We obtain the condition for the manifold with a non-symmetric non-metric connection to be projectively flat and conformally flat. Also, it has been demonstrated that the manifold satisfying the condition $\mathcal{\breve{R}^{\dag}\cdot\breve{S}^{\dag}}$=$0$ is an Einstein manifold. Further, by virtue of this result, we found the condition of Ricci soliton in $\beta$-Kenmotsu manifold to be expanding.