Split rank and semisimple automorphism groups of \(G\)-structures
type: Item
instance of: scholarly article
title: Split rank and semisimple automorphism groups of \(G\)-structures
zbMATH Open document ID: 0644.22003
author: Robert J. Zimmer
published in: Journal of Differential Geometry
publication date: 1987-01-01T00:00:00Z
review text: It is proved that if \(H\) is a semisimple Lie group with finite center acting smoothly on a compact manifold \(M\) and preserving a \(G\)-structure on \(M\), where \(G\) is a real algebraic group, then the \(\mathbb R\)-rank of \(H\) is less than or equal to the \(\mathbb R\)-rank of \(G\). The theorem and in fact a stronger assertion was proved earlier (by the same author) under the additional condition that \(H\) defines a volume density.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 4049899
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: G-structure
zbMATH Keywords: real algebraic group
zbMATH Keywords: \(\mathbb R\)-rank
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214441180
OpenAlex ID: W1498277035
Wikidata QID: Q115184678
DOI: 10.4310/JDG/1214441180
description: scientific article; zbMATH DE number 4049899