On Ricci-Bourguignon solitons: Triviality, uniqueness and scalar curvature estimates

Abstract

We study the Ricci-Bourguignon solitons, special solutions to the namesake flow. We obtain conditions that assure that the scalar curvature of the solitons must be constant, forcing that Ricci-Bourguignon soliton must indeed be a Ricci soliton and, in some special cases, trivial. In addition, we obtain some sufficient conditions for the validity of a weak maximum principle for the weighted Laplacian over the soliton. As a consequence, we get triviality and uniqueness results, as well as estimates for the scalar curvature.