The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups

We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenber...

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Veröffentlicht in:Журнал математической физики, анализа, геометрии
Datum:2006
1. Verfasser: Petrov, Ye.V.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2006
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/106591
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Petrov, Ye.V.
author_facet Petrov, Ye.V.
citation_txt The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ.
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container_title Журнал математической физики, анализа, геометрии
description We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenberg group we also give necessary and su cient conditions for the Gauss map to be harmonic and prove that for m = 1 all CMC-surfaces with the harmonic Gauss map are cylinders .
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language English
last_indexed 2025-12-07T18:02:18Z
publishDate 2006
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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spelling Petrov, Ye.V.
2016-09-30T20:39:21Z
2016-09-30T20:39:21Z
2006
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups / Ye.V. Petrov // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 186-206. — Бібліогр.: 14 назв. — англ.
1812-9471
https://nasplib.isofts.kiev.ua/handle/123456789/106591
We consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric. We derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the 2m+1-dimensional Heisenberg group we also give necessary and su cient conditions for the Gauss map to be harmonic and prove that for m = 1 all CMC-surfaces with the harmonic Gauss map are cylinders .
en
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Журнал математической физики, анализа, геометрии
The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
Article
published earlier
spellingShingle The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
Petrov, Ye.V.
title The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
title_full The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
title_fullStr The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
title_full_unstemmed The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
title_short The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups
title_sort gauss map of hypersurfaces in 2-step nilpotent lie groups
url https://nasplib.isofts.kiev.ua/handle/123456789/106591
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