A trivial projective change of a Finsler metric F is the Finsler metric F+df. I explain when it is possible to make a given Finsler metric both
forward and backward complete by a trivial projective change.
The problem actually came from lorentz geometry and mathematical relativity:
it was observed that it is possible to understand the light-line geodesics of a
(normalized, standard) stationary 4-dimensional space-time as geodesics of a
certain Finsler Randers metric on a 3-dimensional manifold. The trivial
projective change of the Finsler metric corresponds to the choice of another
3-dimensional slice, and the existence of a trivial projective change that is
forward and backward complete is equivalent to the global hyperbolicity of the
space-time.Comment: 11 pages, one figure, submitted to the proceedings of VI
International Meeting on Lorentzian Geometry (Granada