Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606095 | Differential Geometry and its Applications | 2012 | 18 Pages |
Abstract
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 Rapcsák conditions, some peculiarities of the two-dimensional case, and geodesic convexity for sprays.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Crampin, T. Mestdag, D.J. Saunders,