关键词: 近Ricci-Bourguignon孤立子, 射影向量场, 共形Killing, K-切触

Abstract: By using the method of geometric analysis, we study Ricci-Bourguignon almost solitons with projective vector field. Firstly, if the potential vector field is projective one, we prove that the Ricci-Bourguignon almost solitons have vanishing Cotton tensor field, divergence-free Bach tensor field and Ricci tensor field is conformal Killing tensor field. Secondly,  we prove the K-contact Ricci-Bourguignon almost soliton whose potential vector field is a projective vector field is an Einstein mainfold.

Key words: Ricci-Bourguignon almost soliton, projective vector field, conformal Killing, K-contact