Certain triviality results for Ricci-Bourguignon almost solitons

Abstract

In this paper, we study Ricci-Bourguignon soliton and Ricci-Bourguignon almost soliton on a Riemannian manifold and prove some triviality results. First, we derive some sufficient conditions for which a Ricci-Bourguignon soliton or Ricci-Bourguignon almost soliton is trivial. Then we proved that a compact Ricci-Bourguignon almost soliton is isometric to a Euclidean sphere if it has constant scalar curvature or satisfies an integral inequality.