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