Topology of Dupin hypersurfaces with six distinct principal curvatures
type: Item
instance of: scholarly article
title: Topology of Dupin hypersurfaces with six distinct principal curvatures
zbMATH Open document ID: 0928.53028
DOI: 10.1007/PL00004742
published in: Mathematische Zeitschrift
publication date: 2000-01-02T00:00:00Z
review text: The classification of isoparametric and, more generally, of compact (proper) Dupin hypersurfaces in spheres with four and six distinct principal curvatures is still an open problem. In the present paper, the author classifies the homeomorphism types of Dupin hypersurfaces with six different principal curvatures and proves that they are homeomorphic to the known examples. There are two cases: either the dimension of the hypersurface is six and it is even diffeomorphic to \(SU(2)\times SU(2)/Q_8\) where \(Q_8=\{\pm 1,\pm i,\pm j,\pm k\}\), or its dimension is twelve and it is homeomorphic to a principal orbit of the adjoint representation of \(G_2\).
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1336882
zbMATH Keywords: Dupin hypersurfaces
zbMATH Keywords: multiplicities of principal curvatures
author: Fuquan Fang
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: pl00004742
OpenAlex ID: W2009962042
description: scientific article; zbMATH DE number 1336882