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The Arnold-Gelfand Mathematical Seminars pp 77–92Cite as

Crofton Densities, Symplectic Geometry and Hilbert’s Fourth Problem

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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.

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References

  1. Álvarez, J.C. The Symplectic Geometry of Spaces of Geodesics. Ph.D. Thesis, Rutgers University, 1995.

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  3. Àlvarez, J.C., Gelfand, I.M., Smirnov, M. Crofton Densities, Symplectic Geometry, and Hilbert’s Fourth Problem. In preparation.

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Author information

Authors and Affiliations

  1. Dept. of Math., Rutgers University, 08903, New Brunswick, NJ, USA

    J. C. Alvarez

  2. Dept. of Math., Rutgers University, 08903, New Brunswick, NJ, USA

    I. M. Gelfand

  3. Dept. of Math, Columbia University, 10027, New York, NY, USA

    M. Smirnov

Authors
  1. J. C. Alvarez
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  2. I. M. Gelfand
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  3. M. Smirnov
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Editor information

Editors and Affiliations

  1. Ceremade, Université Paris-Dauphine, 75775, Paris Cedex 16, France

    V. I. Arnold

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    I. M. Gelfand

  3. Department of Mathematics, Harvard University, 02139, Cambridge, MA, USA

    V. S. Retakh

  4. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    M. Smirnov

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© 1997 Birkhäuser Boston

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Alvarez, J.C., Gelfand, I.M., Smirnov, M. (1997). Crofton Densities, Symplectic Geometry and Hilbert’s Fourth Problem. In: Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds) The Arnold-Gelfand Mathematical Seminars. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4122-5_2

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  • DOI: https://doi.org/10.1007/978-1-4612-4122-5_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8663-9

  • Online ISBN: 978-1-4612-4122-5

  • eBook Packages: Springer Book Archive

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