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Desarguesian Spaces

  • Herbert Busemann
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 54)

Abstract

An n-dimensional desarguesian space is a metrization of an open subset of the n-dimensional projective space P n as a G-space R whose geodesics fall on projective lines. R is either the entire P n and the geodesics are all isometric to one circle, or R is straight and may be regarded as an open convex set C of the n-dimensional affine space A n with the intersections of the affine Unes with C as geodesies, see Sections 12–14 in G or (8.2) here.

Keywords

Great Circle Projective Line Nonpositive Curvature Universal Covering Space Open Hemisphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Herbert Busemann
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA

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