Skip to main content
SpringerLink
Log in

Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. H. Alexander, “Holomorphic mappings from the ball and polydisc,”Math. Ann.,209, 249–256 (1976).

    Article  MathSciNet  Google Scholar 

  2. R. A. Airapetyan and G. M. Henkin, “Analytic continuation of CR functions through the edge-of-thewedge,”Sov. Math. Dokl.,24, 128–132 (1981).

    Google Scholar 

  3. R. A. Airapetyan and G. M. Henkin, “Integral representations of differential forms at Cauchy-Riemann manifolds and the theory of CR-functions {I, II},”Russ. Math. Surveys. 39, 41–118 (1984):Math. USSR Sb.,55, 91–111 (1986).

    Article  MathSciNet  Google Scholar 

  4. D. N. Akhiezer, “Homogeneous complex spaces,” In:Enc. Math. Sci., Vol. 10, Springer (1990), pp. 195–244.

  5. S. Baouendi, H. Jacobowitz, and F. Trèves, “On the analyticity of CR mappings,”Ann. Math.,122, 365–400 (1985).

    Article  MATH  Google Scholar 

  6. S. Baouendi and F. Trèves, “A property of the functions and distributions annihilated by a locally integrable system of complex vectorfields,”Ann. Math.,113, 387–421 (1981).

    Article  MATH  Google Scholar 

  7. V. K. Belošapka, “Finite-dimesionality of the automorphism group of a real-analytic surface,”Math. USSR Izv.,32, 443–448 (1989).

    Article  MathSciNet  Google Scholar 

  8. V. K. Belošapka, “A uniqueness theorem for automorphisms of a nondegenerate surface in the complex space,”Math. Notes,47, 239–242 (1990).

    MathSciNet  Google Scholar 

  9. V. K. Belošapka, “On holomorphic transformations of a quadric,”Math. USSR Sb.,72, 189–205 (1992).

    Article  MathSciNet  Google Scholar 

  10. S. Bochner and W. T. Martin,Several complex variables, Princeton University Press (1948).

  11. A. Bogges and J. C. Polking, “Holomorphic extension of CR-functions,”Duke Math. J.,49, 757–784 (1982).

    Article  MathSciNet  Google Scholar 

  12. A. Borel, “Kählerian coset spaces of semisimple Lie groups,”Proc. Natl. Acad. Sci. USA,40, 1147–1151 (1954).

    Article  MATH  MathSciNet  Google Scholar 

  13. R. B. Brown, “A minimal representiation for the Lie algebrasE 7,”Ill. J. Math.,12, 190–200 (1968).

    MATH  Google Scholar 

  14. É. Cartan, “Sur les espaces de Riemann dans lesquels le transport par parallélism conservela courbure,”Rend. Acc. Lincei,3, 544–547 (1926).

    MATH  Google Scholar 

  15. É. Cartan, “Sur une classe remarquable d'espaces de Riemann,”Bull. Soc. Math. France,54, 214–264 (1926).

    MATH  MathSciNet  Google Scholar 

  16. É. Cartan, “La géométrie des groupes de transformations,”J. Math. Pures Appl.,6, 1–119 (1927).

    MATH  MathSciNet  Google Scholar 

  17. É. Cartan, “La géométrie des groupes simples,”Ann. Mat. Pura Appl.,4, 209–256 (1927).

    Article  MATH  MathSciNet  Google Scholar 

  18. É. Cartan, “Sur certaines formes Riemanniennes remarquables des géométries a groupe fondamental simple,”Ann. Sci. École Norm. Sup.,44, 345–467 (1927).

    MATH  MathSciNet  Google Scholar 

  19. É. Cartan, “Sur une classe remarquable d'espaces de Riemann,”Bull. Soc. Math. France,55, 114–134 (1927).

    MATH  MathSciNet  Google Scholar 

  20. É. Cartan, “Complément au mémoire ‘sur la géométrie des groupes simples’,”Ann. Mat. Pura Appl.,5, 253–260 (1928).

    Article  MATH  MathSciNet  Google Scholar 

  21. S. S. Chern and J. K. Moser, “Real hypersurfaces in complex manifolds,”Acta Math.,133, 219–271 (1974).

    Article  MathSciNet  Google Scholar 

  22. C. Chevalley and R. D. Schafer, “The exceptional Lie algebrasF 4 andF 6,”Proc. Natl. Acad. Sci. USA,36, 137–141 (1956).

    Article  MathSciNet  Google Scholar 

  23. J. Cima and T. J. Suffridge, “A reflection principle with applications to proper holomorphic mappings,”Math. Ann.,256, 489–500 (1983).

    Article  MathSciNet  Google Scholar 

  24. J. Dorfmeister, “Quasisymmetric Siegel domains and the automorphisms of homogeneous Siegel domains,”Amer. J. Math.,102, 537–563 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  25. J. Dorfmeister, “Homogeneous Siegel domains,”Nagoya Math. J.,86, 39–83 (1982).

    MATH  MathSciNet  Google Scholar 

  26. V. V. Ežov and G. Schmalz,Automorphisms of nondegenerate CR quadrics and Siegel domains. Explicit description, Preprint MPI/94-63, Max-Planck-Institut für Mathematik, Bonn (1994).

    Google Scholar 

  27. V. V. Ežov and G. Schmalz, “Holomorphic automorphisms of quadrics,”Math. Z.,216, 453–470 (1994).

    MathSciNet  MATH  Google Scholar 

  28. V. V. Ežov and G. Schmalz, “Poincaré automorphisms for nondegenerate CR quadrics,”Math. An.,298, 79–87 (1994).

    Article  MATH  Google Scholar 

  29. V. V. Ežov and G. Schmalz, “A simple proof of Belošapka's theorem on the parametrization of the automorphism group of CR-manifolds,”mat. Zametki, to appear.

  30. V. V. Ežov and G. Schmalz, “A matrix Poincaré formula for holomorphic automorphisms of quadrics of higher codimension. Real associative quadrics,”J. Geom. Analysis, to appear.

  31. F. Forstnerič, “Extending proper holomorphic mappings of positive codimension,”Invent. Math.,95, 31–62 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  32. F. Forstnerič, “Mappings of quadric Cauchy-Riemann manifolds,”Math. Ann.,292, 163–180 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  33. S. G. Gindikin, “Analysis in homogeneous domains,”Russian Math. Surveys,19, 1–89 (1964).

    Article  MathSciNet  Google Scholar 

  34. S. G. Gindikin, I. I. Piatetskii-Shapiro, and E. B. Vinberg, “Classification and canonical realization of complex bounded homogeneous domains,”Trans. Moscow Math. Soc.,12, 404–437 (1963).

    Google Scholar 

  35. M. Hakim, “Applications holomorphes propres continues de domaines pseudoconvexes de ℂn dans la boule unite de ℂn+1,”Duke Math. J.,60, 115–133 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  36. J.-I. Hano, “On Kählerian homogeneous spaces of unimodular Lie groups,”Amer. J. Math.,79, 885–900 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  37. Harish-Chandra, “Representations of semi-simple Lie groups IV–VI,”J. Math. IV,77; 743–777; 1–41; 564–628 (1955; 1956; 1956).

    MathSciNet  MATH  Google Scholar 

  38. S. Helgason,Differential Geometry and Symmetric Spaces, Academic Press, New York-London (1962).

    MATH  Google Scholar 

  39. G. M. Henkin and A. E. Tumanov, “Local characterization of holomorphic automorphisms of Siegel domains,”Funct. Analysis,17, 285–294 (1983).

    MATH  MathSciNet  Google Scholar 

  40. Hua Loo Keng,Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, AMS, Providence (1963).

    Google Scholar 

  41. M. Ise, “On canonical realizations of bounded symmetric domains as matrix-spaces,”Nagoya J. Math.,42, 115–133 (1971).

    MATH  MathSciNet  Google Scholar 

  42. W. Kaup, Y. Matsushima, and T. Ochiai, “On the automorphisms and equivalences of generalized Siegel domains,”Amer. J. Math.,92, 475–497 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  43. J. L. Koszul, “Sur la form hermitienne canonique des espaces homogenes complexes,”Can. J. Math.,7, 562–576 (1955).

    MATH  MathSciNet  Google Scholar 

  44. S. Murakami, “On automorphisms of Siegel domains,”Lect. Notes Math.,286, Springer (1972).

  45. I. Naruki, “Holomorphic extension problem for standard real submanifolds of the second kind,”Publ. Res. Inst. Math. Sci.,6, 113–187 (1970).

    MATH  MathSciNet  Google Scholar 

  46. N. Palinčak, “On quadrics of high codimension,”Mat. Zametki. 55, 110–115 (1994).

    Google Scholar 

  47. D. Pelles, “Proper holomorphic self-maps of the unit ball,”Math. Ann.,190, 298–305 (1971).

    Article  MathSciNet  Google Scholar 

  48. I. I. Pyatetskii-Shapiro, “On a problem of É. Cartan,”Dokl. Akad. Nauk SSSR,124, 272–273 (1959).

    MATH  MathSciNet  Google Scholar 

  49. I. I. Pyatetskii-Shapiro,Automorphic Functions and Geometry of Classical Domains, Gordon and Breach New York (1969).

    MATH  Google Scholar 

  50. V. Rabotin. In:Holomorphic Mappings of Complex Manifolds and Related Extremal Problems [in Russian], PhD thesis, Novosibirsk (1986).

  51. I. Satake,Algebraic Structures of Symmetric Domains, Iwanami Shoten and Princeton University Press (1980).

  52. B. Segre, “Intorno al problem di Poincaré della representazione pseudo-conform,”Rend. Acad. Lincei. 13, 676–683 (1931).

    MATH  Google Scholar 

  53. S. Ševčenko, “Description of the algebra of infinitesimal automorphisms of CR-quadrics of codimension two and their classification,”Mat. Zametki,55, 142–153 (1994).

    Google Scholar 

  54. A. Sukhov, “On the mapping problem for quadric Cauchy-Riemann manifolds,”Indiana Univ. Math. J.,42, 27–36 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  55. A. Sukhov, “On CR mappings of real quadric manifolds,”Mich. Math. J.,41, 143–150 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  56. N. J. Tanaka, “On the pseudo-conformal geometry of hypersurfaces of the space ofn complex variables,”J. Math. Soc. Jpn.,14, 397–429 (1962).

    MATH  Google Scholar 

  57. N. J. Tanaka, “On infinitesimal automorphisms of Siegel domains,”J. Math. Soc. Jpn.,22, 180–212 (1970).

    Article  MATH  Google Scholar 

  58. A. E. Tumanov, “The geometry of CR-manifolds,” In:Enc. Math. Sci., Vol. 9, Springer (1989), pp. 201–221.

  59. A. E. Tumanov, “Finite dimensionality of the group of CR-automorphisms of a standard CR manifold and proper holomorphic mappings of Siegel domains,”USSR Izv.,32 (1989).

Download references

Authors
  1. V. V. Ezov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Schmalz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 38. Complex Analysis and Representation Theory-1, 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ezov, V.V., Schmalz, G. Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains. J Math Sci 92, 3712–3763 (1998). https://doi.org/10.1007/BF02434005

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02434005

Keywords

Search

Navigation