Characterizations of Almost Ricci Bourguignon Solitons

TL;DR

This paper explores the properties and classifications of almost Ricci-Bourguignon solitons, clarifying their relation to Einstein-type metrics and extending classical rigidity results for compact cases.

Contribution

It provides new conditions under which compact almost Ricci-Bourguignon solitons are trivial or have special geometric structures, expanding the understanding of these solitons.

Findings

Identifies conditions for triviality of compact almost RB-solitons

Extends classical rigidity theorems to broader settings

Clarifies the position of these solitons within Einstein-type metrics

Abstract

In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify conditions under which a compact almost RB-soliton is trivial or exhibits special geometric properties. We compare our results with classical theorems of Barros and Ribeiro, and explain explicitly how our work extends or complements these earlier findings.