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

TL;DR

This paper investigates a new type of Ricci-Bourguignon almost soliton on Kenmotsu manifolds, deriving scalar curvature, vector field properties, and providing a concrete 5D example to illustrate the theoretical concepts.

Contribution

It introduces and analyzes the $oldsymbol{ abla}$-Ricci-Bourguignon almost soliton in Kenmotsu manifolds, including scalar curvature and vector field characterizations, with a specific 5D example.

Findings

Derived scalar curvature for Kenmotsu manifolds with the soliton.

Characterized vector fields supporting the soliton structure.

Provided a concrete 5D Kenmotsu example.

Abstract

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.