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Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups

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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Main Author: Yampolsky, A.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/106449
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spelling 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
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