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September 2008 Arithmeticity of Totally Geodesic Lie Foliations with Locally Symmetric Leaves
Raul Quiroga-Barranco
Asian J. Math. 12(3): 289-298 (September 2008).

Abstract

Zimmer proved that, on a compact manifold, a foliation with a dense leaf, a suitable leafwise Riemannian symmetric metric and a transverse Lie structure has arithmetic holonomy group. In this work we improve such result for totally geodesic foliations by showing that the manifold itself is arithmetic. This also gives a positive answer, for some special cases, to a conjecture of E. Ghys.

Citation

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Raul Quiroga-Barranco. "Arithmeticity of Totally Geodesic Lie Foliations with Locally Symmetric Leaves." Asian J. Math. 12 (3) 289 - 298, September 2008.

Information

Published: September 2008
First available in Project Euclid: 12 November 2008

zbMATH: 1193.53087
MathSciNet: MR2453557

Subjects:
Primary: 53C12 , 53C24
Secondary: 22E46 , 53C10

Keywords: arithmeticity , foliations , pseudoRiemannian geometry , Semisimple Lie groups , tangential structures , transverse structures

Rights: Copyright © 2008 International Press of Boston

Vol.12 • No. 3 • September 2008
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