Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups
We give a complete list of left-invariant unit vector fields on three-dimensional Lie groups equipped with a left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group equipped with the Sasaki metric. As a result we obtain that each three-dimensional Lie...
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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106449 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups / A. Yampolsky // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 253-276. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106449 |
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dspace |
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irk-123456789-1064492016-09-29T03:02:18Z Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups Yampolsky, A. We give a complete list of left-invariant unit vector fields on three-dimensional Lie groups equipped with a left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group equipped with the Sasaki metric. As a result we obtain that each three-dimensional Lie group admits totally geodesic unit vector eld under some conditions on structural constants. From a geometrical viewpoint, the field is either parallel or a characteristic vector field of a natural almost contact structure on the group. 2007 Article Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups / A. Yampolsky // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 253-276. — Бібліогр.: 9 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106449 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 give a complete list of left-invariant unit vector fields on three-dimensional Lie groups equipped with a left-invariant metric that generate a totally geodesic submanifold in the unit tangent bundle of a group equipped with the Sasaki metric. As a result we obtain that each three-dimensional Lie group admits totally geodesic unit vector eld under some conditions on structural constants. From a geometrical viewpoint, the field is either parallel or a characteristic vector field of a natural almost contact structure on the group. |
| format |
Article |
| author |
Yampolsky, A. |
| spellingShingle |
Yampolsky, A. Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups Журнал математической физики, анализа, геометрии |
| author_facet |
Yampolsky, A. |
| author_sort |
Yampolsky, A. |
| title |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_short |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_full |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_fullStr |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_full_unstemmed |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_sort |
invariant totally geodesic unit vector fields on three-dimensional lie groups |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106449 |
| citation_txt |
Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups / A. Yampolsky // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 253-276. — Бібліогр.: 9 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT yampolskya invarianttotallygeodesicunitvectorfieldsonthreedimensionalliegroups |
| first_indexed |
2023-10-18T20:12:58Z |
| last_indexed |
2023-10-18T20:12:58Z |
| _version_ |
1796149277792141312 |