The multiplier approach to the projective Finsler metrizability problem

Details The multiplier approach to the projective Finsler metrizability problem The multiplier approach to the projective Finsler metrizability problem

2012-03-14

arxiv.org/abs/1203.3142v1

Mathematics

Differential Geometry

25 pages

Scientific paper

This paper is concerned with the problem of determining whether a projective-equivalence class of sprays is the geodesic class of a Finsler function. We address both the local and the global aspects of this problem. We present our results entirely in terms of a multiplier, that is, a type (0,2) tensor field along the tangent bundle projection. In the course of the analysis we consider several related issues of interest including the positivity and strong convexity of positively-homogeneous functions, the relation to the so-called Rapcs\'ak conditions, some peculiarities of the two-dimensional case, and geodesic convexity for sprays.

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