Asian Journal of Mathematics

Volume 12 (2008)

Number 3

Arithmeticity of Totally Geodesic Lie Foliations with Locally Symmetric Leaves

Pages: 289 – 298

DOI: http://dx.doi.org/10.4310/AJM.2008.v12.n3.a2

Author

Raul Quiroga-Barranco

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.

Keywords

Semisimple Lie groups; arithmeticity; foliations; transverse structures; tangential structures; pseudoRiemannian geometry

2010 Mathematics Subject Classification

Primary 53C12, 53C24. Secondary 22E46, 53C10.

Full Text (PDF format)