Almost Ricci-Yamabe solitons on Almost Kenmotsu manifolds

This paper examines almost Kenmotsu manifolds (briefly, AKMs) endowed with the almost Ricci-Yamabe solitons (ARYSs) and gradient ARYSs. The condition for an AKM with ARYS to be eta-Einstein is established. We also show that an ARYS on Kenmotsu manifold becomes a Ricci-Yamabe soliton under certain restrictions. In this series, it is proven that a (2n+1)-dimensional (K, mu)'-AKM equipped with a gradient ARYS is either locally isometric to Hn+1(-4) x R-n or the Reeb vector field and the soliton vector field are codirectional. The properties of three-dimensional non-Kenmotsu AKMs endowed with a gradient ARYS are studied.