Submanifolds with the Harmonic Gauss Map in Lie Groups
In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifo...
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| Дата: | 2008 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106507 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Submanifolds with the Harmonic Gauss Map in Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 278-293. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106507 |
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dspace |
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irk-123456789-1065072016-09-30T03:02:54Z Submanifolds with the Harmonic Gauss Map in Lie Groups Petrov, Ye.V. In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifolds in Lie groups admitting biinvariant metrics. We show that, depending on the structure of the tangent space of a submanifold, the Gauss map can be harmonic in all biinvariant metrics or nonharmonic in some metric. For 2-step nilpotent groups we prove that the Gauss map of a geodesic is harmonic if and only if it is constant. 2008 Article Submanifolds with the Harmonic Gauss Map in Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 278-293. — Бібліогр.: 10 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106507 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 |
In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifolds in Lie groups admitting biinvariant metrics. We show that, depending on the structure of the tangent space of a submanifold, the Gauss map can be harmonic in all biinvariant metrics or nonharmonic in some metric. For 2-step nilpotent groups we prove that the Gauss map of a geodesic is harmonic if and only if it is constant. |
| format |
Article |
| author |
Petrov, Ye.V. |
| spellingShingle |
Petrov, Ye.V. Submanifolds with the Harmonic Gauss Map in Lie Groups Журнал математической физики, анализа, геометрии |
| author_facet |
Petrov, Ye.V. |
| author_sort |
Petrov, Ye.V. |
| title |
Submanifolds with the Harmonic Gauss Map in Lie Groups |
| title_short |
Submanifolds with the Harmonic Gauss Map in Lie Groups |
| title_full |
Submanifolds with the Harmonic Gauss Map in Lie Groups |
| title_fullStr |
Submanifolds with the Harmonic Gauss Map in Lie Groups |
| title_full_unstemmed |
Submanifolds with the Harmonic Gauss Map in Lie Groups |
| title_sort |
submanifolds with the harmonic gauss map in lie groups |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106507 |
| citation_txt |
Submanifolds with the Harmonic Gauss Map in Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 278-293. — Бібліогр.: 10 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
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AT petrovyev submanifoldswiththeharmonicgaussmapinliegroups |
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2023-10-18T20:13:06Z |
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2023-10-18T20:13:06Z |
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