The purpose of the paper is to study Yamabe solitons on three-dimensional para-Sasakian, paracosymplectic and para-Kenmotsu manifolds. Mainly, we proved that *If the semi-Riemannian metric of a three-dimensional para-Sasakian manifold is a Yamabe soliton, then it is of constant scalar curvature, and the flow vector field V is Killing. In the next step, we proved that either manifold has constant curvature -1 and reduces to an Einstein manifold, or V is an infinitesimal automorphism of the paracontact metric structure on the manifold. *If the semi-Riemannian metric of a three-dimensional paracosymplectic manifold is a Yamabe soliton, then it has constant scalar curvature. Furthermore either manifold is $\eta$-Einstein, or Ricci flat. *If the semi-Riemannian metric on a three-dimensional para-Kenmotsu manifold is a Yamabe soliton, then the manifold is of constant sectional curvature -1, reduces to an Einstein manifold. Furthermore, Yamabe soliton is expanding with $\lambda$=-6 and the vector field V is Killing. Finally, we construct examples to illustrate the results obtained in previous sections.

中文翻译：

---

Yamabe 孤子在三维正态几乎平行接触度量流形上

本文的目的是研究三维准 Sasakian、准辛和准剑茂流形上的 Yamabe 孤子。主要证明了*如果三维准Sasakian流形的半黎曼度量是Yamabe孤子，则它具有恒定标量曲率，并且流矢量场V是Killing。在下一步中，我们证明要么流形具有恒定曲率 -1 并简化为爱因斯坦流形，要么 V 是流形上的平行接触度量结构的无穷小自同构。*如果三维副辛流形的半黎曼度量是 Yamabe 孤子，则它具有恒定的标量曲率。此外，流形是 $\eta$-Einstein 或 Ricci 平坦的。*如果三维准玄武流形上的半黎曼度量是 Yamabe 孤子，那么流形的截面曲率是-1，简化为爱因斯坦流形。此外，Yamabe 孤子以 $\lambda$=-6 扩展，向量场 V 是 Killing。最后，我们构建示例来说明在前几节中获得的结果。