Skip to main content
SpringerLink
Log in

Minimal genus of Klein surfaces admitting an automorphism of a given order

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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. N. L.Alling and N.Greenleaf, Foundations of the theory of Klein surfaces. LNM219, Berlin-Heidelberg-New York 1971.

  2. E. Bujalance, Cyclic groups of automorphisms of compact non-orientable Klein surfaces without boundary. Pacific J. Math.109, 279–289 (1983).

    Google Scholar 

  3. J. J. Etayo, Non-orientable automorphisms of Riemann surfaces. Arch. Math.45, 374–384 (1985).

    Google Scholar 

  4. W. D. Geyer undG. Martens, Überlagerungen berandeter Kleinscher Flächen. Math. Ann.228, 101–111 (1977).

    Google Scholar 

  5. W.Hall, Automorphisms and coverings of Klein surfaces. Ph.D. thesis, Southampton 1978.

  6. W. J. Harvey, Cyclic groups of automorphisms of a compact Riemann surface. Quart. J. Math. Oxford (2)17, 86–97 (1966).

    Google Scholar 

  7. A. Hurwitz, Algebraische Gebilde mit eindeutigen Transformationen in sich. Math. Ann.41, 403–442 (1893).

    Google Scholar 

  8. F.Klein, Über Riemanns Theorie der algebraischen Funktionen und ihrer Integrale. Leipzig 1882.

  9. J. T. Knight, Riemann surfaces of field extensions. Proc. Cambridge Phil. Soc.65, 635–650 (1969).

    Google Scholar 

  10. W. Krull undJ. Neukirch, Die Struktur der absoluten Galoisgruppe über dem Körper 202-01. Math. Ann.193, 197–209 (1971).

    Google Scholar 

  11. G. Martens, Galoisgruppen über aufgeschlossenen reellen Funktionenkörpern. Math. Ann.217, 191–199 (1975).

    Google Scholar 

  12. C. L. May, Automorphisms of compact Klein surfaces with boundary. Pacific J. Math.59, 199–210 (1975).

    Google Scholar 

  13. C. L. May, Cyclic automorphism groups of compact bordered Klein surfaces. Houston J. Math.3, 395–405 (1977).

    Google Scholar 

  14. A. Wiman, Über die hyperelliptischen Kurven und diejenigen vom Geschlechtp=3, welche eindeutige Transformationen in sich zulassen. Bihang Kongl. Svenska Vetenskaps-Akademiens Handlingar, Stockholm 1895/96.

    Google Scholar 

Download references

Author information

Author notes

  1. E. Bujalance

    Present address: Departamento de Matemática Fundamental Facultad de Ciencias, U.N.E.D., 28040, Madrid, Spain

  2. J. J. Etayo & J. M. Gamboa

    Present address: Departamento de Algebra Facultad de C. Matemáticas, Universidad Complutense, 28040, Madrid, Spain

  3. G. Martens

    Present address: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße 1 1/2, D-8520, Erlangen

Authors and Affiliations

    Authors
    1. E. Bujalance
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. J. J. Etayo
      View author publications

      You can also search for this author in PubMed Google Scholar

    3. J. M. Gamboa
      View author publications

      You can also search for this author in PubMed Google Scholar

    4. G. Martens
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    Partially supported by “Comisión Asesora de Investigación Cientifica y Técnica”.

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Bujalance, E., Etayo, J.J., Gamboa, J.M. et al. Minimal genus of Klein surfaces admitting an automorphism of a given order. Arch. Math 52, 191–202 (1989). https://doi.org/10.1007/BF01191274

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01191274

    Keywords

    Search

    Navigation