Clifford systems, algebraically constant second fundamental form and isoparametric hypersurfaces
type: Item
instance of: scholarly article
title: Clifford systems, algebraically constant second fundamental form and isoparametric hypersurfaces
zbMATH Open document ID: 0931.53026
author: Sergio Console
author: Carlos Olmos
published in: Manuscripta Mathematica
publication date: 2000-02-20T00:00:00Z
review text: The main result of the paper is that a submanifold with parallel mean curvature in a real space form, whose second fundamental form has the same algebraic type as the one of a symmetric submanifold, is locally symmetric. As an application, the authors give a new proof of \textit{É. Cartan}'s classification of isoparamametric hypersurfaces in spheres with three different principal curvatures [Math. Z. 45, 335-367 (1939; Zbl 0021.15603)]. It should be pointed out that \textit{N. H. Kuiper} already associated Clifford systems to the more general situation of tight \((n-1)\)-connected \(2n\)-dimensional submanifolds in Section 5B of [Invent. Math. 10, 209-238 (1970; Zbl 0187.18902)].
reviewed by: Gudlaugur Thorbergsson
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1240870
zbMATH Keywords: Clifford systems
zbMATH Keywords: isoparametric hypersurfaces
MaRDI profile type: Publication
full work available at URL: s002290050106
OpenAlex ID: W2104250124
DOI: 10.1007/S002290050106
description: scientific article; zbMATH DE number 1240870