Transverse foliations of T^1 S

This is joint work with Rafael Potrie. We study two dimensional foliations F_1, F_2 of a 3-manifold M so that they have C^1 leaves and they are transverse to each other. The intersection is a one dimensional foliation
G, which subfoliates leaves of F_1, F_2. This is very common, for example when F_1, F_2 are the weak stable and unstable foliations of an Anosov flow in a 3-manifold. We assume that the leaves of F_1, F_2 are Gromov hyperbolic. There are several properties to study. One question is when the foliation G is the flow foliation of a topological Anosov flow. We study the particular case that the manifold is T^1 S, the unit tangent bundle of a closed hyperbolic surface. We show for example that if certain leaf spaces associated with G are Hausdorff, then G is the flow foliation of an Anosov flow.