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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| Published in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Date: | 2006 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106591 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716078205960192 |
|---|---|
| author | Petrov, Ye.V. |
| author_facet | Petrov, Ye.V. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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 .
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| first_indexed | 2025-12-07T18:02:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106591 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T18:02:18Z |
| publishDate | 2006 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups Petrov, Ye.V. |
| title | 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_short | The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups |
| title_sort | gauss map of hypersurfaces in 2-step nilpotent lie groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106591 |
| work_keys_str_mv | AT petrovyev thegaussmapofhypersurfacesin2stepnilpotentliegroups AT petrovyev gaussmapofhypersurfacesin2stepnilpotentliegroups |