Geodesic
Projective metrizability in Finsler geometry
Communications in Mathematics, Tome 20 (2012) no. 1, pp. 63-68

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The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. This paper describes an approach to the problem using an analogue of the multiplier approach to the inverse problem in Lagrangian mechanics.
Classification : 53C60
Keywords: Finsler function; spray; projective equivalence; geodesic path; projective metrizability; Hilbert form 
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Saunders, David. Projective metrizability in Finsler geometry. Communications in Mathematics, Tome 20 (2012) no. 1, pp. 63-68. http://geodesic.mathdoc.fr/item/COMIM_2012__20_1_a6/