On the characterization of Ricci–Bourguignon solitons

We study solitons associated with the Ricci–Bourguignon flow. Firstly, we prove a result for a Ricci–Bourguignon soliton that generalizes a corresponding result for a Ricci soliton. Then, we study radially-flat gradient Ricci–Bourguignon solitons and infer that they are rigid. Finally, we characterize gradient Ricci–Bourguignon solitons endowed with a non-parallel, closed homothetic vector field.