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 $\Cal F$ (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 $\Cal F$. 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 their deformations.

arXiv commentIn French. Improved statements. Main Theorems 10.1 and 13.1 are now proved without any metric condition. Also, some remarks added, typos removed and some references added