In this paper: i) We compute the leafwise cohomology of a complete Riemannian Diophantine flow. ii) We solve explicitly the discrete cohomological equation for the Anosov diffeomorphism on the torus defined by a hyperbolic and diagonalizable matrix whose eigenvalues are all real positive numbers. We use this to solve the continuous cohomological equation of the Anosov flow on the hyperbolic torus obtained from by suspension. This enables us to compute some other geometrical objects associated to the diffeomorphism and the foliation like the invariant distributions and the leafwise cohomology.
Akbar DEHGHAN-NEZHAD. Aziz EL KACIMI ALAOUI. "Équations cohomologiques de flots riemanniens et de difféomorphismes d’Anosov." J. Math. Soc. Japan 59 (4) 1105 - 1134, October, 2007. https://doi.org/10.2969/jmsj/05941105