Integral formulas in $h$-Almost Ricci-Bourguignon solitons

TL;DR

This paper derives integral formulas for compact gradient h-almost Ricci-Bourguignon solitons, generalizing previous results and characterizing the geometry of such solitons under specific conditions.

Contribution

It extends integral formulas to h-almost Ricci-Bourguignon solitons and characterizes their geometry when the potential field is conformal or scalar curvature is constant.

Findings

A compact, non-trivial h-almost Ricci-Bourguignon soliton with dimension ≥ 3 is isometric to a Euclidean sphere under certain conditions.

Generalization of integral formulas for these solitons.

Provides conditions under which the solitons are geometrically rigid.

Abstract

The aim of this paper is to investigate some integral formulas for compact gradient $h$-almost Ricci-Bourguignon solitons. Consequently, we generalize the results previously ob tained for Ricci almost solitons. Moreover, we prove that a compact, non-trivial $h$-almost Ricci-Bourguignon soliton with dimension greater than or equal to 3 is isometric to a Euclidean sphere, provided either the potential vector field is conformal or its scalar curvature is constant. Finally, we generalize the integral formula for compact h-almost Ricci-Bourguignon.