Open Access
Feb 2005 Symplectic Geometry and Hilbert's Fourth Problem
J.C. Álvarez Paiva
J. Differential Geom. 69(2): 353-378 (Feb 2005). DOI: 10.4310/jdg/1121449109


Inspired by Hofer's definition of a metric on the space of compactly supported Hamiltonian maps on a symplectic manifold, this paper exhibits an area-length duality between a class of metric spaces and a class of symplectic manifolds. Using this duality, it is shown that there is a twistor-like correspondence between Finsler metrics on ℝPn whose geodesics are projective lines and a class of symplectic forms on the Grassmannian of 2-planes in ℝn+1.


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J.C. Álvarez Paiva. "Symplectic Geometry and Hilbert's Fourth Problem." J. Differential Geom. 69 (2) 353 - 378, Feb 2005.


Published: Feb 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1088.53047
MathSciNet: MR2169868
Digital Object Identifier: 10.4310/jdg/1121449109

Rights: Copyright © 2005 Lehigh University

Vol.69 • No. 2 • Feb 2005
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