Results in Mathematics

, Volume 59, Issue 3–4, pp 301–318 | Cite as

On Möbius Spaces Admitting Automorphism Groups of Type II.2

Article

Abstract

In 1987 the first author extended C. Hering’s classification for Möbius planes (cf. Hering in Math Z 87:252–262, 1965) to higher dimensional Möbius spaces (cf. Kroll in Result Math 12:357–365, 1987). Actually the classification was done for groups of automorphisms of a Möbius space. In this paper we are concerned with Möbius spaces admitting a group of type II.2. Our main result is a generalization of a result of Yaqub (Math Z 142:281–292, 1975, Theorem 1).

Mathematics Subject Classification (2010)

Primary 51F15 Secondary 20N05 

Keywords

Möbius space Möbius plane Hering classification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hartmann E.: Ovoide und Möbius-Ebenen über konvexen Funktionen. Geom. Dedicata 15, 377–388 (1984)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Heise W.: Eine Definition des Möbiusraumes. Manuscripta Math. 2, 39–47 (1970)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Hering C.: Eine Klassifikation der Möbius-Ebenen. Math. Z. 87, 252–262 (1965)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Karzel H., Sörensen K., Windelberg D.: Einführung in die Geometrie. Vandenhoek und Ruprecht, Göttingen (1973)MATHGoogle Scholar
  5. 5.
    Kroll H.-J.: Zur Klassifikation der Möbius-Räume. Result. Math. 12, 357–365 (1987)MATHMathSciNetGoogle Scholar
  6. 6.
    Leichtweiß K.: Konvexe Mengen. Springer, Berlin (1980)Google Scholar
  7. 7.
    Mäurer H.: Ein axiomatischer Aufbau der mindestens 3-dimensionalen Möbius Geometrie. Math. Z. 103, 282–305 (1967)CrossRefGoogle Scholar
  8. 8.
    Yaqub J.C.D.S.: Strongly ovoidal Möbius planes. Math. Z. 142, 281–292 (1975)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenMunichGermany
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

Personalised recommendations