Annali di Matematica Pura ed Applicata

, Volume 139, Issue 1, pp 15–43 | Cite as

Embeddability of smooth Cauchy-Riemann manifolds

  • Roman Dwilewicz


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.


Opposite Sign Complex Manifold Real Dimension Levi Form Global Embeddability 


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© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • Roman Dwilewicz
    • 1
  1. 1.WarsawPoland

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