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: Yampolsky, A.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
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
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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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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