Perturbations of constant connection Wagner spaces.(English)Zbl 1149.53014

Sabau, Sorin V. (ed.) et al., Finsler geometry, Sapporo 2005. In memory of Makoto Matsumoto. Proceedings of the 40th Finsler symposium on Finsler geometry, Sapporo, Japan, September 6–10, 2005. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-42-6/hbk). Advanced Studies in Pure Mathematics 48, 197-224 (2007).
M. Matsumoto proved that any $$2$$-spray is projectively a geodesic spray of a Finsler manifold [Math. Comput. Modelling 20, No. 4–5, 1–23 (1994; Zbl 0812.53022)]. This result was refined, by the first author of this paper and others to the case of constant coefficients sprays, all of which are projectively equivalent to straight lines [Nonlinear Anal. 37, 545–566 (1999)].
In the present paper, the authors classify $$2$$-sprays whose coefficients are linear in $$x^{1}, x^{2}$$, (the adapted coordinates), by a perturbation technique. They also study the Feynman-Kac solutions to the corresponding Finslerian diffusions.
For the entire collection see [Zbl 1130.53005].

MSC:

 53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics) 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 53-04 Software, source code, etc. for problems pertaining to differential geometry

Zbl 0812.53022