Crofton Densities, Symplectic Geometry and Hilbert’s Fourth Problem

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


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.


Symplectic Form Symplectic Geometry Finsler Metrics Oriented Line Natural Identification 
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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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