On manifolds locally modelled on non-Riemannian homogeneous spaces
type: Item
instance of: scholarly article
title: On manifolds locally modelled on non-Riemannian homogeneous spaces
zbMATH Open document ID: 0852.22011
DOI: 10.1007/BF01902217
author: François Labourie
author: Robert J. Zimmer
author: Shahar Mozes
published in: Geometric and Functional Analysis. GAFA
publication date: 1996-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/58215
review text: The investigation of compact manifolds locally modeled on a homogeneous space of a finite dimensional Lie group is continued. The aim of this paper is threefold. First, the proof of the main result of a previous paper [\textit{R. J. Zimmer}, J. Am. Math. Soc. 7, 159-168 (1994; Zbl 0801.22009)] is drastically simplified. The approach considered in the present paper enables to use Moore's ergodicity theorem in place of Ratner's theorem which is required in the proof given in the above mentioned paper. The superrigidity property for cocycles is used in proving the main result. Second, using the new approach, the results of the previous paper are extended to a more general situation. In particular, it is shown that \(SL (m) \backslash SL(2m)\) does not admit a cocompact lattice, nor does \(J \backslash SL(2m)\) where \(J \subset SL(m)\) is either \(SO(p,q)\), \(p + q = m\), or \(Sp(2r,R)\) with \(2r = m\). Third, all these results are generalized to the case of compact forms. Nonconnected algebraic hulls are also considered.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 881242
zbMATH Keywords: compact manifolds
zbMATH Keywords: homogeneous space
zbMATH Keywords: Lie group
zbMATH Keywords: ergodicity theorem
zbMATH Keywords: superrigidity property
zbMATH Keywords: compact forms
zbMATH Keywords: algebraic hulls
Wikidata QID: Q61773413
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: On homogeneous model spaces of compact manifolds
cites work: Q3808879
cites work: Q4314293
cites work: Discrete Groups and Non-Riemannian Homogeneous Spaces
cites work: Q3944785
OpenAlex ID: W2028485962
description: scientific article; zbMATH DE number 881242