This paper is dedicated to the memory of Makoto Matsumoto, Finsler teacher and friend. Prof. Matsumoto augmented work of Darboux and proved that any 2-spray is projectively a geodesic spray of a Finsler manifold, . This result has a refinement for the case of constant coefficient sprays, all of which are projectively equivalent to straight lines, .
In the present paper, we classify 2-sprays whose coefficients are linear in $x^1$, $x^2$, the adapted coordinates, by a perturbation technique. We also study the Feynman-Kac solutions to the corresponding Finslerian diffusions. The results herein arose from applications, especially , , , , .
The computations in this work have been performed by the computer package Finsler , .
Digital Object Identifier: 10.2969/aspm/04810197