Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric
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.
scientific article; zbMATH DE number 1982563