Topological description of Riemannian foliations with dense leaves

Jesús A. Álvarez López and Alberto Candel

Vol. 248 (2010), No. 2, 257–276

DOI: 10.2140/pjm.2010.248.257

Abstract

A foliation is called Riemannian if its holonomy pseudogroup consists of local isometries for some Riemannian metric. By combining the work on Hilbert’s fifth problem for local groups with our work on equicontinuous foliated spaces, we prove that, if a foliated space is strongly equicontinuous, locally connected and of finite dimension, has a dense leaf, and has holonomy pseudogroup whose closure is quasianalytic, then it is a Riemannian foliation.

Keywords

Riemannian foliations, equicontinuous pseudogroups, Hilbert’s fifth problem

Mathematical Subject Classification 2000

Primary: 22E05, 57R30, 57S05, 58H99

Milestones

Received: 4 September 2009

Revised: 22 December 2009

Accepted: 1 February 2010

Published: 1 December 2010