We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

中文翻译：

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齐次三流形中的恒定平均曲率球体

我们证明任意均匀三流形中具有相同恒定平均曲率的两个球体仅因环境等距而不同，并且我们确定存在此类球体的平均曲率值。这给出了三维齐次流形中浸入式恒定平均曲率球体的完整分类。