Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation
type: Item
instance of: scholarly article
title: Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation
zbMATH Open document ID: 0697.53032
DOI: 10.1007/BF02764968
author: Pierre Pansu
author: Robert J. Zimmer
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let \({\mathcal F}\) and \({\mathcal F}'\) be \(C^ 1\)-equivalent foliations of a compact manifold M. Assume that the foliations are equipped with smooth Riemannian metrics along the leaves which vary continuously in the transverse direction. Theorem. If the leaves of \({\mathcal F}\) and \({\mathcal F}'\) are locally isometric to: 1) a quaternionic hyperbolic space of dimension \(\leq 8\), or 2) a Cayley hyperbolic plane, or 3) a real or complex hyperbolic space of dimension \(\leq 3\), then \({\mathcal F}\) and \({\mathcal F}'\) are metrically equivalent provided, in the case (3), that \({\mathcal F}\) admits a holonomy invariant transverse measure.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4142948
zbMATH Keywords: \(C^ 1\)-equivalent foliations
zbMATH Keywords: Riemannian metrics along the leaves
zbMATH Keywords: hyperbolic space
zbMATH Keywords: holonomy invariant transverse measure
reviewed by: Paweł Walczak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4142948