Sur des variétés de Cauchy-Riemann dont la forme de Levi a une valeur propre positive

For certain real hypersurfaces in the projective space, of signature (1, n), we study the filling problem for small deformations of the CR structure (the other signatures being well understood). We characterize the deformations which are fillable, and prove that they have infinite codimension in the set of all CR structures. This result generalizes the cases of the 3-sphere and of signature (1, 1) to higher dimension. © Springer-Verlag 2004.