We give a complete classification of the immersed constant mean curvature spheres in a three-sphere with an arbitrary homogenous metric, by proving that for each $H\in\mathbb{R}$, there exists a constant mean curvature $H$-sphere in the space that is unique up to an ambient isometry.

中文翻译：

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均匀三球中的恒定平均曲率球

我们通过证明对于每个 $H\in\mathbb{R}$，存在一个恒定平均曲率在环境等距的独特空间中。