The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenber...
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| Опубліковано в: : | Журнал математической физики, анализа, геометрии |
|---|---|
| Дата: | 2006 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/106591 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-106591 |
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Petrov, Ye.V. 2016-09-30T20:39:21Z 2016-09-30T20:39:21Z 2006 The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106591 We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenberg group we also give necessary and su cient conditions for the Gauss map to be harmonic and prove that for m = 1 all CMC-surfaces with the harmonic Gauss map are cylinders . en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| spellingShingle |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Petrov, Ye.V. |
| title_short |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| title_full |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| title_fullStr |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| title_full_unstemmed |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| title_sort |
gauss map of hypersurfaces in 2-step nilpotent lie groups |
| author |
Petrov, Ye.V. |
| author_facet |
Petrov, Ye.V. |
| publishDate |
2006 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenberg group we also give necessary and su cient conditions for the Gauss map to be harmonic and prove that for m = 1 all CMC-surfaces with the harmonic Gauss map are cylinders .
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/106591 |
| citation_txt |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ. |
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2025-12-07T18:02:18Z |
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2025-12-07T18:02:18Z |
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