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Characterizations of $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds

Soumendu Roy, Karthika Ramasamy, Lavanya Kumar, Purabi Jana

TL;DR

The paper investigates $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds, establishing when such solitons compress, balance, or enlarge via the parameter $\Omega$ and deriving relations involving the star-curvature $r^*$ and the star-Ricci tensor $\mathbb{S}^*$. It shows that a Kenmotsu manifold admitting a $\ast$-RB soliton often reduces to an $\eta$-RB soliton with explicit constants, and it derives gradient and conformal Killing vector field implications, including a key Laplacian equation $\Delta f=\Omega(2n+1)+[\omega(2n+1)-1](r+4n^2)$. Curvature constraints such as $\mathcal{W}_2$-flatness and $Q$-flatness are analyzed, yielding explicit expressions for $\Omega$ in terms of invariants like $\psi$ and $r$, and criteria for soliton behavior. A concrete $5$-dimensional example verifies the existence of a $\ast$-RB soliton, and the work discusses potential physical applications in areas like string theory and general relativity where soliton structures are relevant.

Abstract

In this paper, we have found some features of $\ast$- Ricci Bourguignon Soliton on Kenmotsu manifold. We estimated the conditions for $\ast$-Ricci Bourguignon on Kenmotsu manifold to be compressing, balancing or enlarging accordingly. We have found some curvature properties of Kenmotsu manifold admitting $\ast$-Ricci Bourguignon Soliton. Additionally, we have featured $\ast$-Ricci Bourguignon on Kenmotsu manifold with torse-forming vector field. Finally, we proved an example of $5$-dimensional Kenmotsu manifold on $\ast$-Ricci Bourguignon Soliton.

Characterizations of $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds

TL;DR

The paper investigates -Ricci-Bourguignon solitons on Kenmotsu manifolds, establishing when such solitons compress, balance, or enlarge via the parameter and deriving relations involving the star-curvature and the star-Ricci tensor . It shows that a Kenmotsu manifold admitting a -RB soliton often reduces to an -RB soliton with explicit constants, and it derives gradient and conformal Killing vector field implications, including a key Laplacian equation . Curvature constraints such as -flatness and -flatness are analyzed, yielding explicit expressions for in terms of invariants like and , and criteria for soliton behavior. A concrete -dimensional example verifies the existence of a -RB soliton, and the work discusses potential physical applications in areas like string theory and general relativity where soliton structures are relevant.

Abstract

In this paper, we have found some features of - Ricci Bourguignon Soliton on Kenmotsu manifold. We estimated the conditions for -Ricci Bourguignon on Kenmotsu manifold to be compressing, balancing or enlarging accordingly. We have found some curvature properties of Kenmotsu manifold admitting -Ricci Bourguignon Soliton. Additionally, we have featured -Ricci Bourguignon on Kenmotsu manifold with torse-forming vector field. Finally, we proved an example of -dimensional Kenmotsu manifold on -Ricci Bourguignon Soliton.
Paper Structure (7 sections, 8 theorems, 75 equations)

This paper contains 7 sections, 8 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Certain results concerning Kenmotsu Manifold equipped with $\ast$- RB Soliton
  4. Some well-known curvature properties on Kenmotsu manifold satisfying $\ast$-RB soliton
  5. Results on torse forming vector field on Kenmotsu manifold equipped with $\ast$-Ricci Bourguignon soliton
  6. Examples of a $5$-dimensional Kenmotsu manifold admitting $\ast$-Ricci Bourguignon soliton
  7. Real world Implementations

Key Result

Theorem 3.1

Suppose the metric $g$ of odd dimensional Kenmotsu Manifold assures $\ast$-Ricci Bourguignon soliton $(g,z,\Omega,\omega)$ then the soliton changes to an $\eta$-RB Soliton $(g,z,\Lambda,\mu,\omega)$ where

Theorems & Definitions (13)

  • Definition 1.1
  • Theorem 3.1
  • Corollary 3.2
  • Theorem 3.3
  • Remark 3.4
  • Definition 3.5
  • Theorem 3.6
  • Definition 4.1
  • Theorem 4.2
  • Definition 4.3
  • ...and 3 more