Variétés CR polarisées et G-polarisées, partie I

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Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation 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 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.