Reductive compact homogeneous CR manifolds

Abstract

We consider a class of compact homogeneous CR manifolds, that we call $\mathfrak{n}$-reductive, which includes the orbits of minimal dimension of a compact Lie group $K_0$ 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 $S^3\to {\mathbb{CP}}^1$. In general these fibrations are not $CR$ submersions, however they satisfy a weaker condition that we introduce here, namely they are CR-deployments.

35 pages