Characterization of Almost η-Ricci-Yamabe Soliton and Gradient Almost η-Ricci-Yamabe Soliton on Almost Kenmotsu Manifolds

The prime object in this article is to study an almost eta-Ricci-Yamabe soliton and gradient almost eta-Ricci-Yamabe soliton within the framework of almost Kenmotsu manifolds. It is shown that normal almost Kenmotsu manifold admitting an almost eta-Ricci-Yamabe soliton or gradient.Ricci-Yamabe soliton is locally isometric to hyperbolic space H2n+1 (-1). Next, we prove that if a (kappa, mu) almost Kenmotsu manifold admits an almost eta-Ricci-Yamabe soliton, then the manifold is eta-Einstein. Besides, we find the condition for non-normal almost Kenmotsu manifolds acknowledging gradient almost eta-Ricci-Yamabe soliton. Moreover, an almost eta-Ricci-Yamabe soliton on (kappa, mu)'-almost Kenmotsu manifold has been studied. Lastly, we construct an example of a gradient almost eta-RicciYamabe soliton on a 3-dimensional Kenmotsu manifold.