Submanifolds with the Harmonic Gauss Map in Lie Groups

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2008
• ISSN: 1812-9471
• Main Author: Petrov, Ye.V.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106507
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Submanifolds with the Harmonic Gauss Map in Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 278-293. — Бібліогр.: 10 назв. — англ.

In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifo...