Vol. 248, No. 2, 2010

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Topological description of Riemannian foliations with dense leaves

Jesús A. Álvarez López and Alberto Candel

Vol. 248 (2010), No. 2, 257–276

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.

Riemannian foliations, equicontinuous pseudogroups, Hilbert’s fifth problem
Mathematical Subject Classification 2000
Primary: 22E05, 57R30, 57S05, 58H99
Received: 4 September 2009
Revised: 22 December 2009
Accepted: 1 February 2010
Published: 1 December 2010
Jesús A. Álvarez López
Departamento de Xeometría e Topoloxía
Facultade de Matemáticas
Universidade de Santiago de Compostela
Campus Universitario Sur
15706 Santiago de Compostela
Alberto Candel
Department of Mathematics
California State University
Northridge, CA 91330
United States