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VOL. 48 | 2007 Perturbations of constant connection Wagner spaces
Peter L. Antonelli, Solange F. Rutz

Editor(s) Sorin V. Sabau, Hideo Shimada


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, [12]. This result has a refinement for the case of constant coefficient sprays, all of which are projectively equivalent to straight lines, [5].

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 [3], [4], [7], [10], [14].

The computations in this work have been performed by the computer package Finsler [1], [13].


Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1149.53014
MathSciNet: MR2389256

Digital Object Identifier: 10.2969/aspm/04810197

Keywords: 2 dimensional classification , constant connections , Finsler geometry and diffusion , Wagner spaces

Rights: Copyright © 2007 Mathematical Society of Japan


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