Almost Kenmotsu $$(k,\mu )'$$-manifolds with Yamabe solitons

Abstract

Let $$(M^{2n+1},\phi ,\xi ,\eta ,g)$$ be a non-Kenmotsu almost Kenmotsu $$(k,\mu )'$$ -manifold. If the metric g represents a Yamabe soliton, then either $$M^{2n+1}$$ is locally isometric to the product space $$\mathbb {H}^{n+1}(-4)\times \mathbb {R}^n$$ or $$\eta $$ is a strict infinitesimal contact transformation. The later case can not occur if a Yamabe soliton is replaced by a gradient Yamabe soliton. Some corollaries of this theorem are given and an example illustrating this theorem is constructed.