Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and \(N\)-wave systems
type: Item
instance of: scholarly article
title: Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and \(N\)-wave systems
zbMATH Open document ID: 0872.53005
DOI: 10.1016/0926-2245(95)00022-4
published in: Differential Geometry and its Applications
publication date: 1996-07-07T00:00:00Z
review text: The author investigates low-dimensional homogeneous isoparametric hypersurfaces in connection with a Hamiltonian system on the ambient Euclidean space. Let \(M\) be an isoparametric hypersurface with \(g\) distinct principal curvatures and multiplicities \(m_1\), \(m_2\). For the cases \((g,m_1,m_2)=(3,1,1), (3,2,2), (4,1,1), (4,1,2), (4,1,3), (4,2,2), (6,1,1)\) the author gives explicit descriptions of the Cartan-Münzner polynomials. The corresponding symmetric space is then used to show that the Hamiltionian system is integrable, but not diagonalizable. Further possible generalizations are pointed out. The paper is clearly written and contains 58 references.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 897458
zbMATH Keywords: homogeneous isoparametric hypersurfaces
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Cartan-Münzner polynomials
Wikidata QID: Q115362555
author: E. V. Ferapontov
reviewed by: Linus Kramer
MaRDI profile type: Publication
full work available at URL: 0926-2245(95)00022-4
OpenAlex ID: W2013798651
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description: scientific article; zbMATH DE number 897458