Asian Journal of Mathematics
Volume 12 (2008)
Arithmeticity of Totally Geodesic Lie Foliations with Locally Symmetric Leaves
Pages: 289 – 298
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.
Semisimple Lie groups; arithmeticity; foliations; transverse structures; tangential structures; pseudoRiemannian geometry
2010 Mathematics Subject Classification
Primary 53C12, 53C24. Secondary 22E46, 53C10.