Lorentzian isoparametric hypersurfaces in \(H_1^{n+1}\)
A hypersurface in an anti-de Sitter sphere \(H_1^{n+1}\) is called isoparametric if the minimal polynomial of the shape operator is constant. This allows complex or non-simple principal curvatures. In this paper, the local classification of the Lorentzian isoparametric hypersurfaces in \(H_1^{n+1}\) is obtained. More precisely, we show that there are four types of such hypersurfaces. Type I hypersurfaces are determined by two orthogonal subspaces of \(\mathbb{R}_2^{n+2}\) and the principal curvatures; type II and type III hypersurfaces are determined by two 1-parameter orthogonal subspaces of \(\mathbb{R}_2^{n+2}\) and the principal curvatures; and the type IV hypersurfaces are homogeneous.
scientific article; zbMATH DE number 1186482