Geometriae Dedicata

, Volume 72, Issue 3, pp 283–297

16-Dimensional Smooth Projective Planes with Large Collineation Groups

  • Richard Bödi

DOI: 10.1023/A:1005020223604

Cite this article as:
Bödi, R. Geometriae Dedicata (1998) 72: 283. doi:10.1023/A:1005020223604


Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such that the geometric operations of join and intersection are smooth. A systematic study of such planes and of their collineation groups can be found in previous works of the author. We prove in this paper that a 16-dimensional smooth projective plane which admits a collineation group of dimension d ≥ 39 is isomorphic to the octonion projective plane P2 O. For topological compact projective planes this is true if d ≥ 41. Note that there are nonclassical topological planes with a collineation group of dimension 40.

smooth projective plane homogeneity 16-dimensional. 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Richard Bödi
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany; e-mail

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