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Geodesics of two-dimensional Finsler spaces. (English) Zbl 0812.53022

Summary: A concise description of 2-dimensional Finsler spaces is presented from the viewpoint of their geodesic curves (i.e., extremals of a variational problem). Berwald’s classification and geodesics of 1-form metric spaces are studied. Darboux’s solution to the problem of determination of the variational functional (homogeneous Lagrangian) from given geodesic equations is presented.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53C22 Geodesics in global differential geometry
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