Connection preserving actions of lattices in \(SL_ n\mathbb{R}{}\)
type: Item
instance of: scholarly article
title: Connection preserving actions of lattices in \(SL_ n\mathbb{R}{}\)
zbMATH Open document ID: 0786.57016
DOI: 10.1007/BF02764799
author: Renato Feres
published in: Israel Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: The author studies connection-preserving actions of lattice subgroups of \(\text{SL}_ n(\mathbb{R})\), \(n\geq 3\), on compact Riemannian manifolds \(M\). The main result gives a description of such actions as follows: If \(\dim M=n+1\), then either the action preserves a smooth invariant Riemannian metric on \(M\) or it can be described in terms of linear actions on the \(n\)-torus.
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 219381
zbMATH Keywords: connection-preserving actions of lattice subgroups of \(\text{SL}_ n(\mathbb{R})\) on compact Riemannian manifolds
zbMATH Keywords: linear actions on the \(n\)- torus
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
cites work: Anosov Diffeomorphisms on Tori
cites work: Rigidity for Anosov actions of higher rank lattices
cites work: Local rigidity for certain groups of toral automorphisms
cites work: Global rigidity results for lattice actions on tori and new examples of volume-preserving actions
cites work: Q3997989
cites work: Cartan subgroups and lattices in semi-simple groups
cites work: Ergodic theory of differentiable dynamical systems
cites work: On connection-preserving actions of discrete linear groups
cites work: Q3687381
cites work: Q3812470
full work available at URL: https://doi.org/10.1007/bf02764799
OpenAlex ID: W2068923114
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description: scientific article; zbMATH DE number 219381