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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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.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 |
irk-123456789-106591 |
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irk-123456789-1065912016-10-01T03:02:21Z The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Petrov, Ye.V. 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 . 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106591 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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 . |
| format |
Article |
| author |
Petrov, Ye.V. |
| spellingShingle |
Petrov, Ye.V. The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Журнал математической физики, анализа, геометрии |
| author_facet |
Petrov, Ye.V. |
| author_sort |
Petrov, Ye.V. |
| title |
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| 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 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Журнал математической физики, анализа, геометрии |
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AT petrovyev thegaussmapofhypersurfacesin2stepnilpotentliegroups AT petrovyev gaussmapofhypersurfacesin2stepnilpotentliegroups |
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2023-10-18T20:13:17Z |
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2023-10-18T20:13:17Z |
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