Embeddability of Smooth Cauchy-Riemann Manifolds
The main purpose of this paper is to give a sufficient condition for global embeddability of smooth Cauchy-Riemann manifolds (CR-manifolds) into complex manifolds with boundary. Namely, let M be a smooth CR-manifold of real dimension 2n − 1 and CR-dimension n − 1, where n ⩾ 2, which is locally CR-embeddable into a complex manifold. Assume further that the Levi form of M is non-vanishing at each point. The main result of this paper is that such a CR-manifold is globally CR-embeddable into an n-dimensional complex manifold with boundary. Moreover if the Levi form has at each point of M eigenvalues of opposite signs, then M embeds into a complex manifold without boundary.
R. Dwilewicz, "Embeddability of Smooth Cauchy-Riemann Manifolds," Annali di matematica Pura ed Applicata, Springer Verlag, Jan 1985.
The definitive version is available at http://dx.doi.org/10.1007/BF01766848
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