On almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci-Bourguignon solitons
Moctar Traore, Hakan Mete Taştan, Sibel Gerdan Aydın
Abstract
We investigate a Riemannian manifold with almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci-Bourguignon soliton structure. We use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci-Bourguignon soliton. Moreover, we show that a nontrivial, compact almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci-Bourguignon soliton of constant scalar curvature is isometric to the Euclidean sphere. Using some results obtaining from almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci Bourguignon soliton, we give the integral formulas for compact orientable almost <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Ricci-Bourguignon soliton.