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Arithmeticity of totally geodesic Lie foliations with locally symmetric leaves

Raul Quiroga-Barranco
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Abstract

R. 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.

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BibTeXRIS

Raul Quiroga-Barranco. 2007-01-08. Arithmeticity of totally geodesic Lie foliations with locally symmetric leaves. https://arxiv.org/abs/math/0701233

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