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 $\ast$-$k$-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting $\ast$-$k$-Ricci-Yamabe soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies $\ast$-$k$-Ricci-Yamabe soliton. 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 have studied gradient $\ast$-$\eta$-Einstein soliton to yield the nature of Riemannian curvature tensor. We have developed an example of $\ast$-$k$-Ricci-Yamabe soliton on 5-dimensional Kenmotsu manifold to prove our findings.

arXiv admin note: text overlap with arXiv:2105.11142, arXiv:2105.13885, arXiv:2109.04700

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