Arithmeticity of totally geodesic Lie foliations with locally symmetric leaves

Details Arithmeticity of totally geodesic Lie foliations with locally symmetric leaves Arithmeticity of totally geodesic Lie foliations with locally symmetric leaves

2007-01-08

arxiv.org/abs/math/0701233v1

Asian J. Math. 12 (2008), no. 3, 289-297

Mathematics

Differential Geometry

Scientific paper

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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