Abelian extensions of semisimple graded CR algebras

In this paper we take up the problem of describing the CR vector bundles M over compact standard CR manifolds S, which are themselves standard CR manifolds. They are associated to special graded Abelian extensions of semisimple graded CR algebras.Comment: 25 pages, 5 figure

On the topology of minimal orbits in complex flag manifolds

We compute the Euler-Poincar\'e characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.Comment: 21 pages v2: Major revisio

The CR structure of minimal orbits in complex flag manifolds

Let \^G be a complex semisimple Lie group, Q a parabolic subgroup and G a real form of \^G. The flag manifold \^G/Q decomposes into finitely many G-orbits; among them there is exactly one orbit of minimal dimension, which is compact. We study these minimal orbits from the point of view of CR geometry. In particular we characterize those minimal orbits that are of finite type and satisfy various nondegeneracy conditions, compute their fundamental group and describe the space of their global CR functions. Our main tool are parabolic CR algebras, which give an infinitesimal description of the CR structure of minimal orbits.Comment: AMS-TeX, 44 pages v2: minor revisio