%0 Journal Article
%T Asymmetry in Hilbert's fourth problem
%A Juan-Carlos Alvarez Paiva
%J Mathematics
%D 2013
%I arXiv
%X In the asymmetric setting, Hilbert's fourth problem asks to construct and study all (non-reversible) projective Finsler metrics: Finsler metrics defined on open, convex subsets of real projective $n$-space for which geodesics lie on projective lines. While asymmetric norms and Funk metrics provide many examples of essentially non-reversible projective metrics defined on proper convex subsets of projective $n$-space, it is shown that any projective Finsler metric defined on the whole projective $n$-space is the sum of a reversible projective metric and an exact 1-form.
%U http://arxiv.org/abs/1301.2524v1