Isoparametric and Dupin Hypersurfaces
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Isoparametric and Dupin Hypersurfaces
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| Creator |
Cecil, T.E.
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| Description |
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 deeper and more complex for hypersurfaces in the sphere Sn. A hypersurface Mn−1 in a real space-form is proper Dupin if the number g of distinct principal curvatures is constant on Mn−1, and each principal curvature function is constant along each leaf of its corresponding principal foliation. This is an important generalization of the isoparametric property that has its roots in nineteenth century differential geometry and has been studied effectively in the context of Lie sphere geometry. This paper is a survey of the known results in these fields with emphasis on results that have been obtained in more recent years and discussion of important open problems in the field.
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| Date |
2019-02-19T12:58:42Z
2019-02-19T12:58:42Z 2008 |
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| Type |
Article
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| Identifier |
Isoparametric and Dupin Hypersurfaces / T.E. Cecil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 171 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 53C40; 53C42; 53B25 http://dspace.nbuv.gov.ua/handle/123456789/149015 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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