Hilbert forms for a Finsler metrizable projective class of sprays (Q1940114)

In terms of 2-forms on the slit tangent bundle, the authors establish necessary and sufficient conditions under which a projective-equivalence class of sprays is the geodesic class of a Finsler function, (so called metrizability conditions). Also, the relations between the known results [\textit{I. Bucataru} and \textit{Z. Muzsnay}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 114, 22 p. (2011; Zbl 1244.49072); \textit{J. C. Álvarez Paiva}, J. Differ. Geom. 69, No. 2, 353--378 (2005; Zbl 1088.53047)] are emphasized and it is shown that they are equivalent.