Reductive compact homogeneous CR manifolds

We consider a class of compact homogeneous CR manifolds, that we call n-reductive, which includes the orbits of minimal dimension of a compact Lie group K0 in an algebraic homogeneous variety of its complexification K. For these manifolds we define canonical equivariant fibrations onto complex flag manifolds. The simplest example is the Hopf fibration S 3 → CP1. In general these fibrations are not CR submersions, however they satisfy a weaker condition that we introduce here, namely they are CR-deployments.