Generalized k-Contact Structures

With the goal to study and better understand algebraic Anosov actions of R k , we develop a higher codimensional analogue of the contact distribution on odd dimensional manifolds, call such structure a generalized k -contact structure.We show that there exist an R k -action associated with this structure, afterwards, we relate this structure with the Weyl chamber actions and a few more general algebraic Anosov actions, proving that such actions admits a compatible generalized k -contact structure.