Let (X,ω0) be a compact complex manifold of complex dimension n endowed with a Hermitian metric ω0. The Chern-Yamabe problem is to find a conformal metric of ω0 such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

中文翻译：

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Chern-Yamabe 问题和 Chern-Yamabe 孤子

让(X,ω0)是复维数的紧复流形n具有厄米特度量ω0. Chern-Yamabe 问题是找到一个保形度量ω0这样它的陈标量曲率是恒定的。在本文中，我们证明了 Chern-Yamabe 问题的解在某些条件下是唯一的。另一方面，我们得到了一些与 Chern-Yamabe 孤子相关的结果。