摘要: The examples given by Nirenberg in [5] and [6] show that not all three dimensional CR manifolds may be realized as real hypersurfaces 1172. These are perturbations of the structure on sphere. In this paper we extend his construction any strictly pseudo-convex realizable dimension 3 perturbed so to obtain a non-realizable one. This is done Sect. 1. 2 non-realizability for higher structures provided Levi form non-degenerate has only one positive eigenvalue, our last section summarize Cartan's approach geometry. From viewpoint it was important decide if Nirenberg's example really limited We have made self-contained proofs several known results. For instance Lemma 1.l, first part 1.5 were proved Lewy [2]. And 1.2 well observation hypersurface convex some coordinate system,