A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\: \textbf{Q}\phi=\phi \textbf{Q}$

Abstract

In the present paper, we prove that if the metric of a three dimensional almost Kenmotsu manifold with $\textbf{Q}\phi=\phi \textbf{Q}$ whose scalar curvature remains invariant under the chracterstic vector field $\zeta$, admits a non-trivial Yamabe solitons, then the manifold is of constant sectional curvature or the manifold is Ricci simple.