Geodesic rays in locally symmetric spaces
type: Item
instance of: scholarly article
title: Geodesic rays in locally symmetric spaces
zbMATH Open document ID: 0846.53032
DOI: 10.1016/0926-2245(96)00007-1
author: Enrico Leuzinger
published in: Differential Geometry and its Applications
publication date: 1996-08-05T00:00:00Z
review text: Let \(X\) be an irreducible Riemannian symmetric space of noncompact type and of rank \(\geq 2\). Consider a locally symmetric quotient \(V = \Gamma \backslash X\) by a discrete group of isometries \(\Gamma\) of \(X\). The arithmeticity theorem of Margulis asserts that if the volume of \(V\) is finite, then the lattice \(\Gamma\) is arithmetic. This imposes a \(\mathbb{Q}\)-structure on the group of isometries of \(X\), which is reflected in the geometry of \(V\). In the present paper we give a detailed description of geodesic rays in the ends (or cusps) of \(V\). Technically our approach is based on a differential geometric interpretation of well-known facts from the (algebraic) reduction theory of arithmetic groups. As an application we study the ``Tits geometry'' of such locally symmetric spaces \(V\).
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 897466
zbMATH Keywords: locally symmetric space
zbMATH Keywords: ends of manifolds of nonpositive curvature
zbMATH Keywords: Tits buildings
zbMATH Keywords: arithmetic groups
Wikidata QID: Q115362515
MaRDI profile type: Publication
full work available at URL: 0926-2245(96)00007-1
OpenAlex ID: W1980320772
cites work: Q5580322
cites work: Some metric properties of arithmetic quotients o f symmetric spaces and an extension theorem
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cites work: Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
cites work: Groupes reductifs
cites work: Q3997989
cites work: Kazhdan groups acting on compact manifolds
cites work: Geometry of compactifications of locally symmetric spaces
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description: scientific article; zbMATH DE number 897466