Regularity of foliations and Lyapunov exponents of partially hyperbolic dynamics on 3-torus

In this work we study the relation between the regularity of invariant foliations and the Lyapunov exponents of partially hyperbolic diffeomorphisms. We suggest a new regularity condition for foliations in terms of disintegration of the Lebesgue measure which can be considered to be a criterium for the rigidity of Lyapunov exponents.