We obtain a classification result for rotational surfaces in Berger spheres, whose mean curvature is given as a prescribed function of their angle function. Under hypothesis on the prescribed function, we show that these surfaces behave like the Delaunay surfaces of constant mean curvature. The classification is done by means of a phase plane analysis of the ODE fulfilled by the profile curve of such surfaces.

中文翻译：

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Berger 球体中规定平均曲率的 Delaunay 曲面

我们获得了 Berger 球体中旋转表面的分类结果，其平均曲率作为其角度函数的规定函数给出。在对指定函数的假设下，我们表明这些曲面的行为类似于具有恒定平均曲率的 Delaunay 曲面。分类是通过 ODE 的相平面分析完成的，该 ODE 由此类表面的轮廓曲线实现。