manuscripta mathematica

, Volume 115, Issue 4, pp 489–494 | Cite as

Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

Article

Abstract.

We give a simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into a generic real algebraic CR manifold of the same real codimension in a finite dimensional space. In particular, most such germs are not holomorphically equivalent to a germ of a generic real algebraic CR manifold.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baouendi, M.S., Ebenfelt, P., Rothschild, L.P.: Real Submanifolds in Complex Spaces. Princeton Univ. Press, Princeton, New Jersey, 1998Google Scholar
  2. 2.
    Baouendi, M.S., Ebenfelt, P., Rothschild, L.P.: Local geometric properties of real submanifolds in complex space–-a survey. Bull. Am. Math. Soc. 37, 309–336 (2000)CrossRefMATHGoogle Scholar
  3. 3.
    Chern, S.S., Moser, J.K.: Real hypersurfaces in complex manifolds. Acta Math. 133, 219–271 (1974)MATHGoogle Scholar
  4. 4.
    Ebenfelt, P.: On the unique continuation problem for CR mappings into non-minimal hypersurfaces. J. Geom. Anal. 6, 385–405 (1996)MATHGoogle Scholar
  5. 5.
    Forstnerič, F.: Embedding strictly pseudoconvex domains into balls. Trans. Am. Math. Soc. 295, 347–368 (1986)Google Scholar
  6. 6.
    Gaussier, H., Merker, J.: Nonalgebraizable real analytic tubes in Cn. Math. Z. 247, 337–383 (2004)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Grauert, H., Remmert, R.: Analytische Stellenalgebren. Springer-Verlag, Berlin-Heidelberg-New York, 1971Google Scholar
  8. 8.
    Huang, X, Ji, S., Yau, S.S.T.: An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface. Ark. Mat. 39, 75–93 (2001)MATHGoogle Scholar
  9. 9.
    Ji, S.: Algebraicity of real analytic hypersurfaces and blowing-down. J. Geom. Anal. 12, 255–264 (2002)MATHGoogle Scholar
  10. 10.
    Ji, S.: Algebraicity of real analytic hypersurfaces with maximal rank. Am. J. Math. 124, 1083–1102 (2002)MATHGoogle Scholar
  11. 11.
    Lempert, L.: Imbedding strictly pseudoconvex domains into balls. Am. J. Math. 104, 901–904 (1982)MATHGoogle Scholar
  12. 12.
    Poincaré, H.: Les fonctions analytiques de deux variables et la représentation conforme. Rend. Circ. Mat. Palermo (1907), 185–220Google Scholar
  13. 13.
    Webster, S.M.: Some birational invariants for algebraic real hypersurfaces. Duke Math. J. 45, 39–46 (1978)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institute of Mathematics, Physics and MechanicsUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations