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

Abstract

This paper focuses on the study of the newly introduced $\ast -\mathbf{\kappa }$-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 $\ast -\mathbf{\kappa }-$Ricci-Bourguignon soliton. Additionally, we explore applications involving torse-forming vector fields within the framework of the $\ast -\mathbf{\kappa }-$Ricci-Bourguignon almost soliton on Kenmotsu structure manifolds. To support the theoretical findings, we provide a concrete illustration belonging to a $\ast -\mathbf{\kappa }-$Ricci-Bourguignon almost soliton in a 5D Kenmotsu structure manifold.