Isoparametric hypersurfaces with four principal curvatures, IV

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 Münzner. This completes the classification of isoparametric hypersurfaces in spheres that É. Cartan initiated in the late 1930s.

68 pages. Appendix II, which handles the anomalous case in an ad hoc fashion, in the previous version is now removed with the availability of the preprint entitled "Orthogonal multiplications of type $[3,4,p],p\le 12$", arXiv:1705.04762. Accordingly, the Introduction and Section 7, up to and including Remark 7.3., are slightly reworded with no change in all conclusions

References in corpus (1)

• Singular Riemannian foliations and applications to positive and nonnegative curvature

Cited by in corpus (3)

• New examples of Willmore submanifolds in the unit sphere via isoparametric functions,II
• Extrinsic geometry of the Gromoll-Meyer sphere
• Moment maps and Isoparametric hypersurfaces in spheres --- Hermitian cases