Results in Mathematics

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

On Möbius Spaces Admitting Automorphism Groups of Type II.2



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 


Möbius space Möbius plane Hering classification 


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  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

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