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

• 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
• 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.

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...