Isoparametric hypersurfaces with four principal curvatures, IV
Differential Geometry
2017-06-06 v2
Abstract
We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair 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.
Cite
@article{arxiv.1605.00976,
title = {Isoparametric hypersurfaces with four principal curvatures, IV},
author = {Quo-Shin Chi},
journal= {arXiv preprint arXiv:1605.00976},
year = {2017}
}
Comments
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 $[3, 4, p], p\leq 12$", 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