On almost η-Ricci-Bourguignon solitons

We investigate a Riemannian manifold with almost η-Ricci-Bourguignon soliton structure. We use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost η-Ricci-Bourguignon soliton. Moreover, we show that a nontrivial, compact almost η-Ricci-Bourguignon soliton of constant scalar curvature is isometric to the Euclidean sphere. Using some results obtaining from almost η-Ricci Bourguignon soliton, we give the integral formulas for compact orientable almost η-Ricci-Bourguignon soliton.