Variétés CR polarisées et G-polarisées, partie I

Laurent Meersseman (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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. 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.

Domaines: Variables complexes [math.CV]; Géométrie différentielle [math.DG]

Laurent Meersseman. Variétés CR polarisées et G-polarisées, partie I. International Mathematics Research Notices, 2014, 2014 (21), pp.5912-5973. ⟨10.1093/imrn/rnt153⟩. ⟨hal-00761089⟩