Multicontact vector fields on Hessenberg manifolds

In 1850, Liouville proved that any C^4 conformal map between domains in R^3 is necessarily the restriction of the action of one element of O(1,4). Cowling, De Mari, Koranyi and Reimann recently proved a Liouville type result: they defined a generalized contact structure on homogeneous spaces of the type G/P, where G is a semisimple Lie group and P a minimal parabolic subgroup, and they show that the group of contact mappings coincides with G. In this paper, we consider the problem of characterizing the contact mappings on a natural class of submanifolds of G/P, namely the Hessenberg manifolds.