Variétés CR polarisées et G-polarisées, partie I

Abstract

Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution (E,J). Polarized means that (E,J) is roughly speaking invariant by ⁠. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on the existence of a local moduli space.