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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  1. [1]
    A. Andreotti,Introduzione all'analisi complessa, Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e loro Applioazioni, n. 24, Lezioni tenute nel Febbraio 1972, Accademia Nazionale dei Lincei, Koma, 1976.Google Scholar
  2. [2]
    A. Andreotti -G. A. Fredricks,Embeddability of real analytic Cauchy-Riemann manifolds, Ann. Scuola Normale Superiore Pisa,6 (1979), pp. 285–304.Google Scholar
  3. [3]
    A. Andreotti -P. Holm,Quasi-analytic and parametric spaces, in:Singularities of Real Complex Maps, Oslo, 1976, Noordhoof, Leyden, The Netherlands, 1977.Google Scholar
  4. [4]
    L.Boutet de Monvel,Intégration des équations de Cauchy-Riemann induites formelles, Sèminaire Goulaouic-Lions-Schwartz, 1974–1975, Exposé n. 9.Google Scholar
  5. [5]
    F. Bruhat -H. Whitney,Quelques propriétés fondamentales des ensembles analytiquesréels, Comment. Math. Helv.,33 (1959), pp. 132–160.Google Scholar
  6. [6]
    R.Dwilewicz,On the Hans Lewy theorem, will be published in some italian journal.Google Scholar
  7. [7]
    R.Dwilewicz,Complexification of smooth Cauchy-Riemann manifolds, Proceedings of the Seminar on the Monge-Ampère Equation, Florence, October 1980.Google Scholar
  8. [8]
    H. Lewy,On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math.,64 (1956), pp. 514–522.Google Scholar
  9. [9]
    J. R. Munkres,Elementary differential topology, Revised edition, Annals of Mathematics Studies, n. 54, Princeton University Press, Princeton, New Jersey, 1966.Google Scholar
  10. [10]
    L. Nirenberg,Lectures on linear partial differential equations, Regional Conf. Series in Math., n. 17, American Math. Society, Providence, 1973.Google Scholar
  11. [11]
    L. Nirenberg,On a problem of Earns Lewy, Lecture Notes in Math., n. 459 (1975), pp. 224–234, Springer, Berlin-Heidelberg-New York, 1975.Google Scholar
  12. [12]
    R. O. Wells Jr.,Function theory on differentiable submanifolds. Contribution to analysis, A collection of papers dedicated to Lipman Bers, Edited by L.V. Ahlfors, I. Kra, B. Maskit, L. Nirenberg, Academic Press, New York and London, 1974, pp. 407–441.Google Scholar

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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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