Kenmotsu Contact Geometry Through the Lens of $\ast-\boldsymbol{\kappa}$-Ricci-Bourguignon Almost Solitons

This paper focuses on the study of the newly introduced $\ast-\boldsymbol{\kappa}$-Ricci-Bourguignon almost soliton pertaining to Kenmotsu structure manifolds.

Our analysis concerns the characteristics of this soliton and derive the scalar curvature for a Kenmotsu manifold admitting such a structure.

Further, we formulate the corresponding vector fields under the assumption that the manifold supports a $\ast-\boldsymbol{\kappa}-$Ricci-Bourguignon soliton.

Additionally, we explore applications involving torse-forming vector fields within the framework of the $\ast-\boldsymbol{\kappa}-$Ricci-Bourguignon almost soliton on Kenmotsu structure manifolds.

To support the theoretical findings, we provide a concrete illustration belonging to a $\ast-\boldsymbol{\kappa}-$Ricci-Bourguignon almost soliton in a 5D Kenmotsu structure manifold.