Isoparametric and Dupin Hypersurfaces
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...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149015 |
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| Цитувати: | Isoparametric and Dupin Hypersurfaces / T.E. Cecil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 171 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149015 |
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irk-123456789-1490152019-02-20T01:27:05Z Isoparametric and Dupin Hypersurfaces Cecil, T.E. 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. 2008 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cecil, T.E. |
| spellingShingle |
Cecil, T.E. Isoparametric and Dupin Hypersurfaces Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cecil, T.E. |
| author_sort |
Cecil, T.E. |
| title |
Isoparametric and Dupin Hypersurfaces |
| title_short |
Isoparametric and Dupin Hypersurfaces |
| title_full |
Isoparametric and Dupin Hypersurfaces |
| title_fullStr |
Isoparametric and Dupin Hypersurfaces |
| title_full_unstemmed |
Isoparametric and Dupin Hypersurfaces |
| title_sort |
isoparametric and dupin hypersurfaces |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149015 |
| citation_txt |
Isoparametric and Dupin Hypersurfaces / T.E. Cecil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 171 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT cecilte isoparametricanddupinhypersurfaces |
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2023-05-20T17:32:00Z |
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2023-05-20T17:32:00Z |
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1796153499759673344 |