Almost Ricci–Yamabe solitons on almost Kenmotsu manifolds

Abstract

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 [Formula: see text]-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 [Formula: see text]-dimensional [Formula: see text]-AKM equipped with a gradient ARYS is either locally isometric to [Formula: see text] 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.