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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| Published in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Date: | 2007 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106449 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862681095675314176 |
|---|---|
| author | Yampolsky, A. |
| author_facet | Yampolsky, A. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-12-07T15:49:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106449 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T15:49:13Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Yampolsky, A. 2016-09-28T19:09:06Z 2016-09-28T19:09:06Z 2007 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 https://nasplib.isofts.kiev.ua/handle/123456789/106449 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups Article published earlier |
| spellingShingle | Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups Yampolsky, A. |
| title | 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_short | Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups |
| title_sort | invariant totally geodesic unit vector fields on three-dimensional lie groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106449 |
| work_keys_str_mv | AT yampolskya invarianttotallygeodesicunitvectorfieldsonthreedimensionalliegroups |