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

TL;DR

This paper investigates the properties and characterizations of $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds, including scalar curvature, vector fields, and gradient solitons, supported by a concrete 5-dimensional example.

Contribution

It provides new characterizations of $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds, including scalar curvature and vector field properties, with an explicit example.

Findings

Scalar curvature determined for solitons on Kenmotsu manifolds

Characterization of vector fields satisfying the soliton condition

Constructed explicit example of a $*$-$k$-Ricci-Yamabe soliton

Abstract

The goal of the current paper is to characterize $*$-$k$-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 $*$-$k$-Ricci-Yamabe soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies $*$-$k$-Ricci-Yamabe soliton. Also we have embellished some applications of vector field as torse-forming in terms of $*$-$k$-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 $*$-$k$-Ricci-Yamabe soliton on 5-dimensional Kenmotsu manifold to prove our findings.