Let $(X,{\omega }_0)$ be a compact complex manifold of complex dimension $n$ endowed with a Hermitian metric ${\omega }_0$. The Chern-Yamabe problem is to find a conformal metric of ${\omega }_0$ 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 $（X，{\omega }_0）$ 成为具有复杂尺寸的紧凑型复杂流形 $ñ$ 具有厄米度量标准 ${\omega }_0$。Chern-Yamabe问题是要找到一个保形度量${\omega }_0$这样其Chern标量曲率是恒定的。本文证明了在某些情况下解决Chern-Yamabe问题的方法是唯一的。另一方面，我们获得了与Chern-Yamabe孤子有关的一些结果。