Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces
type: Item
instance of: scholarly article
title: Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces
zbMATH Open document ID: 0629.53047
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: The isotropy representations of semisimple symmetric spaces produce orbits in the pseudo-Riemannian sphere. This paper deals with the case that the orbits are homogeneous hypersurfaces. Their geometry is studied, especially the principal curvatures and focal sets. A complete list of homogeneous hypersurfaces that are orbits under isotropy representations of semisimple symmetric spaces is given. In contrast to the positive definite case, not all homogeneous hypersurfaces in the pseudo-Riemannian sphere are orbits under an isotropy representation.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4024231
zbMATH Keywords: isotropy representations
zbMATH Keywords: semisimple symmetric spaces
zbMATH Keywords: homogeneous hypersurfaces
zbMATH Keywords: principal curvatures
zbMATH Keywords: focal sets
zbMATH Keywords: pseudo-Riemannian sphere
author: Jörg M. Hahn
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04020271
OpenAlex ID: W2008799033
DOI: 10.2969/JMSJ/04020271
description: scientific article; zbMATH DE number 4024231