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arXiv · 1605.00976

Isoparametric hypersurfaces with four principal curvatures, IV

Quo-Shin Chi
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Abstract

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 M\"{u}nzner. This completes the classification of isoparametric hypersurfaces in spheres that \'{E}. Cartan initiated in the late 1930s.

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Quo-Shin Chi. 2016-05-03. Isoparametric hypersurfaces with four principal curvatures, IV. https://arxiv.org/abs/1605.00976

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