Advertisement

Division of cauchy-riemann functions on hypersurfaces

  • Roman Dwilewicz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1039)

Abstract

In this paper we discuss the problem of division of two CR functions defined on a smooth hypersurface having the same zero sets. We prove that if the CR differentials of the functions f,g are not singular on the hypersurface, then the quotients f/g, g/f can be extended to smooth CR functions on the whole hypersurface.

Keywords

Complex Manifold Normal Bundle Explicit Definition Levi Form Smooth Hypersurface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Andreotti, G.A. Fredricks, Embeddability of real analytic Cauchy-Riemann manifolds. Ann.Scuola. Norm. Sup. Pisa, 6 (1979), 285–304.MathSciNetzbMATHGoogle Scholar
  2. [2]
    R.Dwilewicz, On the Hans Lewy theorem. To be submitted for publication in an italian journal.Google Scholar
  3. [3]
    R.Dwilewicz, Embeddability of smooth Cauchy-Riemann manifolds. Preprint no.246, Inst. of Math. Polish Academy of Sciences, (1981), 1–86.Google Scholar
  4. [4]
    L. Hörmander, An introduction to complex analysis in several variables. D. Van Nostrand Company, Inc., Princeton, New Jersey, 1966.zbMATHGoogle Scholar
  5. [5]
    L.R. Hunt, R.O, Wells, Jr., Holomorphic extension for nongeneric CR-submanifolds. In: Proceedings of Symposia in Pure Mathematics (Stanford 1973), vol.27, part II, 81–88. Amer. Math. Soc.,Providence, Rhode Island, 1975.Google Scholar
  6. [6]
    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), 514–522.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    A. Newlander, L. Nirenberg, Complex analytic coordinates in almost complex manifolds. Ann. of Math., 65 (1957), 391–404.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    C. Rea, Levi-flat submanifolds and holomorphic extension of foliations. Ann. Scuola Norm. Sup. Pisa, 26 (1972), 665–681.MathSciNetzbMATHGoogle Scholar
  9. [9]
    F. Sommer, Komplex-analytische Blätterung reeler Mannigfaltigkeiten im Cn. Math. Ann. 136 (1958), 111–133.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    R.O. Wells, Jr., Holomorphic hulls and holomorphic convexity of differentiable submanifolds. Trans. Amer. Math. Soc. 132 (1968), 245–262.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    R.O. Wells, Jr., Function theory on differentiable submanifolds. Contribution to Analysis, A collection of papers dedicated to Lipman Bers, Academic Press, New York, 1974, 407–441.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Roman Dwilewicz
    • 1
  1. 1.Institute of MathematicsUniversity of WarsawWarszawaPoland

Personalised recommendations