Geometry of almost $*$-$\eta$-Ricci-Yamabe soliton on Kenmotsu manifolds

Abstract

The goal of the present object in this article is to study of almost $*$-$\eta$-Ricci-Yamabe soliton within the framework of Kenmotsu manifolds. It is shown that if a Kenmotsu manifold admits a $*$-$\eta$-Ricci-Yamabe soliton, then it is $\eta$-Einstein. Next, we prove that if a $(\kappa,2)'$-nullity distribution, where $\kappa<-1$ acknowledges a $*$-$\eta$-Ricci-Yamabe soliton, then the manifold is Ricci flat. Later, if $g$ represents a gradient almost $*$-$\eta$-Ricci-Yamabe soliton and $\xi$ leaves the scalar curvature $r$ invariant on a Kenmotsu manifold, then the manifold is an $\eta$-Einstein. Further, we have studied on a Kenmotsu manifold if $g$ represents an almost $*$-$\eta$-Ricci-Yamabe soliton with potential vector field $V$ is pointwise collinear with $\xi$, then the manifold is an $\eta$-Einstein. Lastly, we give an example of a gradient almost $*$-$\eta$-Ricci-Yamabe soliton on a 5-dimensional Kenmotsu manifold.