Lorentzian isoparametric hypersurfaces in \(H_1^{n+1}\)
type: Item
instance of: scholarly article
title: Lorentzian isoparametric hypersurfaces in \(H_1^{n+1}\)
zbMATH Open document ID: 0923.53023
author: Liang Xiao
published in: Pacific Journal of Mathematics
publication date: 1998-08-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1186482
zbMATH Keywords: isoparametric hypersurface
zbMATH Keywords: Lorentzian isoparametric hypersurface
zbMATH Keywords: Lorentzian space form
MaRDI profile type: Publication
full work available at URL: pjm.1999.189.377
OpenAlex ID: W2058075401
DOI: 10.2140/PJM.1999.189.377
description: scientific article; zbMATH DE number 1186482