The dynamics of quasi-isometric foliations
  If the stable, center, and unstable foliations of a partially hyperbolic system are quasi-isometric, the system has Global Product Structure. This result also applies to Anosov systems and to other invariant splittings.   If a partially hyperbolic system on a manifold with abelian fundamental group has quasi-isometric stable and unstable foliations, the center foliation is without holonomy. If, further, the system has Global Product Structure, then all center leaves are homeomorphic. 
Andy Hammerlindl
math.DS