Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds

Abstract

In this manuscript, we investigate the characterizations of $\ast$-$η$-Schouten solitons on a Kenmotsu manifold when the potential vector field is torse-forming. We determine the nature of the soliton and derive the scalar curvature for a Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton. Further, we establish several conditions associated with the $\ast$-$η$-Schouten soliton. We also study the characterization of the vector field under the assumption that the manifold satisfies the $\ast$-$η$-Schouten soliton equation. Moreover, certain applications of torse-forming vector fields are discussed in the setting of $\ast$-$η$-Schouten solitons on Kenmotsu manifolds. In addition, we examine infinitesimal CL-transformations and the Schouten-Van Kampen connection on Kenmotsu manifolds whose metrics admit $\ast$-$η$-Schouten solitons. Finally, an example of a 3-dimensional Kenmotsu manifold admitting a $\ast$-$η$-Schouten soliton is constructed to verify the obtained results.