REDUCTIVE COMPACT HOMOGENEOUS CR MANIFOLDS

Abstract

We define and investigate a class of compact homogeneous CR manifolds, that we call $$ \mathfrak{n} $$ -reductive. They are orbits of minimal dimension of a compact Lie group K 0 in algebraic affine homogeneous spaces of its complexification K. For these manifolds we obtain canonical equivariant fibrations onto complex flag manifolds, generalizing the Hopf fibration $$ {S^3}\to \mathbb{C}{{\mathbb{P}}^1} $$ . These fibrations are not, in general, CR submersions, but satisfy the weaker condition of being CR-deployments; to obtain CR submersions we need to strengthen their CR structure by lifting the complex stucture of the base.