Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the considered Ricci-like soliton has a constant length and the manifold is $\eta$-Einstein. Other curvature conditions are also found, which imply that the main metric is Einstein. After that, some results are obtained for a parallel symmetric second-order covariant tensor on the manifolds under study. Finally, an explicit example of dimension 5 is given and some of the results are illustrated.

中文翻译：

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在类 Sasaki 类几乎接触 B 度量流形上具有垂直势的类 Ricci 孤子

Sasaki 类几乎接触 B 度量流形上的类 Ricci 孤子是研究的对象。考虑类 Ricci 孤子的势是 Reeb 矢量场或与它共线的情况。在前一种情况下，研究了并行或循环 Ricci 张量的性质。在后一种情况下，表明所考虑的类 Ricci 孤子的势具有恒定长度，流形为 $\eta$-Einstein。还发现了其他曲率条件，这意味着主要度量是爱因斯坦。之后，针对所研究的流形上的平行对称二阶协变张量获得了一些结果。最后，给出了维度 5 的一个明确示例，并说明了一些结果。