Dupin hypersurfaces with six principal curvatures
type: Item
instance of: scholarly article
title: Dupin hypersurfaces with six principal curvatures
zbMATH Open document ID: 0711.53049
published in: Kodai Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The author shows that a Dupin hypersurface with six principal curvatures is Lie equivalent to an isoparametric hypersurface if all cross ratios of sets of four principal curvatures are constant and a certain condition on the intersection properties of curvature leaves is satisfied. This continues the the author's work [ibid., No.2, 228-256 (1989; Zbl 0687.53053)] where a similar theorem was proved for Dupin hypersurfaces with four principal curvatures.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4169612
zbMATH Keywords: Lie sphere geometry
zbMATH Keywords: Dupin hypersurface
zbMATH Keywords: isoparametric hypersurface
author: Reiko Miyaoka
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039098
OpenAlex ID: W2040736577
cites work: Dupin hypersurfaces and a Lie invariant
cites work: Dupin Hypersurfaces
DOI: 10.2996/KMJ/1138039098
description: scientific article; zbMATH DE number 4169612