Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric
type: Item
instance of: scholarly article
title: Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric
zbMATH Open document ID: 1044.53047
published in: Manuscripta Mathematica
publication date: 2003-09-16T00:00:00Z
review text: The authors calculate the Laplacian of the Gauss map for an orientable hypersurface \(M\) in a Lie group \(G\) that possesses a bi-invariant metric. Here the Gauss map is the map that translates the unit normal vector field along \(M\) to the unit sphere in the Lie algebra of \(G\). As an application, they show that \(M\) has constant mean curvature if and only if the Gauss map is harmonic. They obtain further results in the case when \(G\) is three-dimensional.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1982563
zbMATH Keywords: Gauss map
zbMATH Keywords: Lie group
zbMATH Keywords: Laplacian
zbMATH Keywords: harmonic maps
author: Nedir do Espírito-Santo
author: Susana Fornari
author: Katia Frensel
author: Jaime Ripoll
reviewed by: James Hebda
MaRDI profile type: Publication
full work available at URL: s00229-003-0357-5
OpenAlex ID: W2126594774
Wikidata QID: Q115388453
DOI: 10.1007/S00229-003-0357-5
description: scientific article; zbMATH DE number 1982563