Abstract
This paper is concerned with the rigidity problem for volume preserving partially hyperbolic diffeomorphisms on homotopic to a linear Anosov on . We characterize the C1+θ conjugacy of such diffeomorphisms in terms of smooth conditions on the stable and unstable foliations. The smooth conditions on the foliations are to be C1 foliations and transversely absolutely continuous with bounded Jacobians. In particular these conditions for only one direction (stable, centre or unstable) completely determine the Lyapunov exponents.
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