This paper aims to classify a certain type of three-dimensional complete non-Sasakian contact manifold with specific properties, namely \(Q\xi =\sigma \xi \) and admitting Ricci–Bourguignon solitons. In the case of constant \(\sigma \), the paper proves that if the potential vector field of the Ricci–Bourguignon soliton is orthogonal to the Reeb vector field, then the manifold is either Einstein or locally isometric to E(1, 1). Under a similar hypothesis, the paper shows that a \((\kappa ,\mu ,\vartheta )\)-contact metric manifold is locally isometric to E(1, 1). Finally, the paper considers the scenario where the potential vector is pointwise collinear with the Reeb vector field and presents some results.

本文旨在对一类具有特定性质的三维完全非 Sasakian 接触流形进行分类，即\(Q\xi =\sigma \xi \)并承认 Ricci-Bourguignon 孤子。在常数\(\sigma \)的情况下，论文证明，如果 Ricci-Bourguignon 孤子的势向量场与 Reeb 向量场正交，则流形要么是爱因斯坦的，要么是局部等距于E (1, 1 ）。在类似的假设下，论文表明\((\kappa ,\mu ,\vartheta )\)接触度量流形与E (1, 1)局部等距。最后，本文考虑了势向量与 Reeb 向量场逐点共线的情况，并给出了一些结果。