Marked length rigidity for symmetric spaces
type: Item
instance of: scholarly article
title: Marked length rigidity for symmetric spaces
zbMATH Open document ID: 1002.22005
author: Françoise Dal'Bo
author: Inkang Kim
published in: Commentarii Mathematici Helvetici
publication date: 2002-09-25T00:00:00Z
review text: The authors prove a marked-length-spectrum rigidity result for Zariski dense subgroups \(\Gamma\) of a connected semisimple Lie group \(G\) without compact factor and with trivial center. Namely, every surjective homomorphism \(\varphi:\Gamma\to\Gamma'\) between two such subgroups of \(G\), \(G'\) which preserves the translation lengths extends to a continuous isomorphism of \(G\) onto \(G'\). The proof is a remarkably simple application of a result of \textit{Y. Benoist} [Geom. Funct. Anal. 7, 1-47 (1997; Zbl 0947.22003)] on limit cones of Zariski dense subgroups of simple Lie groups of noncompact type.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 1807867
zbMATH Keywords: symmetric spaces
zbMATH Keywords: length spectrum
zbMATH Keywords: rigidity
zbMATH Keywords: Zariski dense subgroups
zbMATH Keywords: semisimple Lie group
MaRDI profile type: Publication
full work available at URL: s00014-002-8346-y
OpenAlex ID: W2076105589
DOI: 10.1007/S00014-002-8346-Y
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description: scientific article; zbMATH DE number 1807867