Transverse minimal foliations on unit tangent bundles of surfaces satisfy a dichotomy (Anosov intersection or Reeb surface), implying that volume-preserving partially hyperbolic diffeomorphisms on these spaces are ergodic.
Calegari, Foliations and the Geometry of 3-Manifolds, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2007
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Transverse minimal foliations on unit tangent bundles and applications
Transverse minimal foliations on unit tangent bundles of surfaces satisfy a dichotomy (Anosov intersection or Reeb surface), implying that volume-preserving partially hyperbolic diffeomorphisms on these spaces are ergodic.