Geometry of $\ast$-$k$-Ricci-Yamabe soliton and gradient $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Abstract

The goal of the current paper is to characterize the $\ast$-$k$-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and found the scalar curvature when the manifold admits the $\ast$-$k$-Ricci-Yamabe soliton on the Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies the $\ast$-$k$-Ricci-Yamabe solitons. Also we have embellished some applications of vector field as torse-forming in terms of $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifold. Then, we studied the gradient $\ast$-$k$-Ricci-Yamabe soliton to yield the nature of the Riemannian curvature tensor. We have developed an example of a $\ast$-$k$-Ricci-Yamabe soliton on a 5-dimensional Kenmotsu manifold to prove our findings.