Isoparametric and Dupin Hypersurfaces

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Author: Cecil, T.E.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149015
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Isoparametric and Dupin Hypersurfaces / T.E. Cecil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 171 назв. — англ.

A hypersurface Mn−1 in a real space-form Rn, Sn or Hn is isoparametric if it has constant principal curvatures. For Rn and Hn, the classification of isoparametric hypersurfaces is complete and relatively simple, but as Élie Cartan showed in a series of four papers in 1938–1940, the subject is much d...