Skip to main content
SpringerLink
Log in

Holomorphic self-maps of parallelizable manifolds

  • Published:
Transformation Groups Aims and scope Submit manuscript

Abstract

We investigate holomorphic self-maps of complex manifolds of the formG/Γ whereG is a complex Lie group and Γ a lattice. We show that they are induced by automorphisms ofG and that a surjective holomorphic self-map can be nonbijective only in the directions of the nilradical ofG.

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

Similar content being viewed by others

References

  1. L. Auslander,On radicals of discrete subgroups of Lie groups, Am. J. Math.85 (1963), 145–150.

    Google Scholar 

  2. W. Barth, M. Otte,Invariante Holomorphe Funktionen auf Reduktiven Liegruppen, Math. Ann.201 (1973), 91–112.

    Google Scholar 

  3. A. Borel,Density properties of certain subgroups of semisimple groups, Ann. of Math.72 (1960), 179–188.

    Google Scholar 

  4. J. Dixmier, W. G. Lister,Derivations of nilpotent Lie algebras, Proc. A.M.S.8 155–158 (1957).

    Google Scholar 

  5. T. Iwamoto,Density properties of complex Lie groups, Osaka J. Math.23 (1986), 859–865.

    Google Scholar 

  6. А. И. Мальцев,Од однот классе однородных пространцтв, ИзВ. АН СССР, сер. матем.13 (1949), 9–32. English translation: A. I. Mal'cev,On a class of homogeneous spaces, AMS Transl., Ser. One9 (1962), 277–307.

    Google Scholar 

  7. G. Margulis,Discrete Subgroups of Semi-Simple Lie Groups, Erg. Math. Springer-Verlag, 1990.

  8. G. D. Mostow,Homogenous spaces of finite invariant measures Ann. of Math. 75 (1962), 17–37.

    Google Scholar 

  9. G. D. Mostow,Arithmetic subgroups of groups with radical, Ann. Math.93 (1971), 409–438.

    Google Scholar 

  10. M. S. Raghunathan,Discrete Subgroups of Lie Groups, Erg. Math. Grenzgeb. Springer, 1972. Russian translation: М. Рагунатан,Дискретные подгруппы грунн Ли, Мир, Москва, 1977.

  11. H. Wang,Complex parallelisable manifolds., Proc. A.M.S.5 (1954), 771–776.

    Google Scholar 

  12. J. Winkelmann,Complex-Analytic Geometry of Complex Parallelizable Manifolds., Habilitationsschrift. Ruhr-Universität Bochum Heft 13 der Schriftenreihe des Graduiertenkolleg., 1995.

Download references

Author information

Authors and Affiliations

  1. Mathematisches Instutut NA 4/69, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    J. Winkelmann

Authors
  1. J. Winkelmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author wishes to thank the Université de Nancy for their invitation during which this manuscript was completed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Winkelmann, J. Holomorphic self-maps of parallelizable manifolds. Transformation Groups 3, 103–111 (1998). https://doi.org/10.1007/BF01237842

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01237842

Keywords

Search

Navigation