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PreprintarXiv licencearXiv

A concise proof of homogeneity of an isoparametric hypersurface with (g, m)=(6, 2)

  • Chao Qian
  • Zizhou Tang
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Abstract

A well-known hypersurface classification theorem states that any isoparametric hypersurface in S13 with six principal curvatures is homogeneous. This landmark result was first proved in her Annals paper in 2013 by R. Miyaoka with 58 pages, and with errata in Annals in 2016 with 15 pages. The main purpose of this paper is to provide a concise proof of this theorem through an interplay between topological and geometric insights into the Euler class of an oriented vector bundle.

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Cite

BibTeXRIS
BibTeX
@misc{qian2026concise,
  title = {{A concise proof of homogeneity of an isoparametric hypersurface with $(g, m)=(6, 2)$}},
  author = {Chao Qian and Zizhou Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.16658},
  eprint = {2609.16658},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16658},
}
RIS
TY  - UNPB
TI  - A concise proof of homogeneity of an isoparametric hypersurface with (g, m)=(6, 2)
AU  - Chao Qian
AU  - Zizhou Tang
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.16658
UR  - https://arxiv.org/abs/2609.16658
AB  - A well-known hypersurface classification theorem states that any isoparametric hypersurface in S^13 with six principal curvatures is homogeneous. This landmark result was first proved in her Annals paper in 2013 by R. Miyaoka with 58 pages, and with errata in Annals in 2016 with 15 pages. The main purpose of this paper is to provide a concise proof of this theorem through an interplay between topological and geometric insights into the Euler class of an oriented vector bundle.
ER  -