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Crofton Densities, Symplectic Geometry and Hilbert’s Fourth Problem

  • J. C. Alvarez
  • I. M. Gelfand
  • M. Smirnov

Abstract

We study the relation between the integral geometric and the symplectic construction of Desarguesian metrics on R n and show that these constructions characterize all Desarguesian Finsler metrics.

Keywords

Symplectic Form Symplectic Geometry Finsler Metrics Oriented Line Natural Identification 
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

© Birkhäuser Boston 1997

Authors and Affiliations

  • J. C. Alvarez
    • 1
  • I. M. Gelfand
    • 2
  • M. Smirnov
    • 3
  1. 1.Dept. of Math.Rutgers UniversityNew BrunswickUSA
  2. 2.Dept. of Math.Rutgers UniversityNew BrunswickUSA
  3. 3.Dept. of MathColumbia UniversityNew YorkUSA

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