Skip to main content
SpringerLink
Log in

Moebius planes with locally euclidean circles are flat

  • Published:
Mathematische Annalen 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. Adams, J. F.: On the nonexistence of elements of Hopf invariant one. Ann. Math.72, 20–104 (1960).

    Google Scholar 

  2. Benz, W.: Über Moebius-Ebenen. J. Ber. DMV63, 1–27 (1960).

    Google Scholar 

  3. Dembowski, P.: Finite geometries. New York: Springer 1968.

    Google Scholar 

  4. Dugundji, J.: Topology. Boston: Allyn and Bacon 1966.

    Google Scholar 

  5. Ewald, G.: Beispiel einer Moebius-Ebene mit nichtisomorphen affinen Unterebenen. Arch. der Math.11, 146–150 (1960).

    Google Scholar 

  6. Ewald, G.: Aus konvexen Kurven bestehende Moebius-Ebenen. Abh. Math. Sem. Hamburg30, 179–187 (1967).

    Google Scholar 

  7. Groh, H.: Topologische Laguerre-Ebenen I. Abh. Math. Sem. Hamburg32, 216–231 (1968).

    Google Scholar 

  8. Groh, H.: Topologische Laguerre-Ebenen II. Abh. Math. Sem. Hamburg34, 11–21 (1969).

    Google Scholar 

  9. Groh, H.: Flat Moebius planes. Geometriae Dedicata1, 65–84 (1972).

    Google Scholar 

  10. Groh, H., Heise, W.: 3-Ovals in Moebius planes. In print in Geometriae Dedicata.

  11. Harrold, O. G.: Pseudo-isotopically contractible spaces. Proc. Amer. Math. Soc.16, 186–187 (1965).

    Google Scholar 

  12. Heise, W.: Zum Begriff der topologischen Moebius-Ebene. Abh. Math. Sem. Hamburg33, 216–224 (1969).

    Google Scholar 

  13. Heise, W.: Eine neue Klasse von Möbiusm-Strukturen. Rend. Ist. Matem. Univ. Trieste2, 125–128 (1970).

    Google Scholar 

  14. James, I. M.: Multiplication on spheres I. Proc. Amer. Math. Soc.8, 192–196 (1957).

    Google Scholar 

  15. Nagata, J.: Modern dimension theory. New York: Wiley 1965.

    Google Scholar 

  16. Salzmann, H.: Topologische projektive Ebenen. Math. Zeitschr.67, 436–466 (1957).

    Google Scholar 

  17. Salzmann, H.: Topological planes. Advances in Mathematics2, 1–60 (1967).

    Google Scholar 

  18. Salzmann, H.: Kompakte vier-dimensionale Ebenen. Arch. der Math.20, 551–555 (1969).

    Google Scholar 

  19. Skornjakov, L. A.: Topological projective planes (Russian). Trudy Moskov Mat. Obšč3, 347–373 (1954).

    Google Scholar 

  20. Strambach, K.: Sphärische Kreisebenen. Math. Zeitschr.113, 266–292 (1970).

    Google Scholar 

  21. Strambach, K.: Sphärische Kreisebenen mit einfacher Automorphismengruppe. Will appear in Geometriae Dedicata.

  22. Strambach, K.: Sphärische Kreisebenen mit nicht-einfacher Automorphismengruppe. Math. Z.124, 289–314 (1972).

    Google Scholar 

  23. Wölk, R.-D.: Topologische Moebiusebenen. Math. Z.93, 311–333 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada

    Hansjoachim Groh

Authors
  1. Hansjoachim Groh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Groh, H. Moebius planes with locally euclidean circles are flat. Math. Ann. 201, 149–156 (1973). https://doi.org/10.1007/BF01359792

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01359792

Keywords

Search

Navigation