We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair $(7, 8)$ is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus, Karcher, and Münzner. This completes the classification of isoparametric hypersurfaces in spheres that É. Cartan initiated in the late 1930s.

中文翻译：

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具有四个主曲率的等参超曲面IV

我们证明具有四个主曲率和多重对$（7，8）$的等参超曲面是由Ozeki和Takeuchi构造的一个，还是由Ferus，Karcher和Münzner构造的两个的其中一个。这样就完成了É球体中等参超曲面的分类。Cartan始于1930年代后期。