In this paper, we obtain the formula of scalar curvature for Kropina metrics. Then we prove that a Kropina metric of isotropic scalar curvature must be of isotropic S-curvature. We also focus on Yamabe problem in Kropina metrics and give a negative answer to the Yamabe problem on Kropina metrics with isotropic S-curvature. It turns out that C-reducible metrics do not satisfy Yamabe problem.

中文翻译：

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Kropina指标的Yamabe问题

在本文中，我们获得了Kropina度量的标量曲率公式。然后我们证明各向同性标量曲率的Kropina度量必须具有各向同性S曲率。我们还关注Kropina度量中的Yamabe问题，并对具有各向同性S曲率的Kropina度量中的Yamabe问题给出否定答案。事实证明，可简化C的度量不能满足Yamabe问题。