Some constructions of projectively flat Finsler metrics
The authors study a projectively flat Finsler metric the geodesics are straight lines. Rapcsak considered the following problem: Given a path with the spray coefficients, find the Finsler spaces whose geodesics are the given paths. He proved a lemma (Rapcsak's lemma) giving the condition that the two Finsler metrics on the same manifold M are pointwisely projective related to each other. G. Hamel found the condition that a Finsler metric \(F=F (x, y)\) is projectively flat. This condition is given by some partial differential equations of the Finsler metric \(F\) on some open domain. The authors find some solutions to Hamel's partial differential equations that characterize the projectively flat Finsler metrics. Further, they find that some of these metrics actually have zero flag curvature. Randers metrics and the deformation of Randers metrics have an important role in this paper.
scientific article; zbMATH DE number 5118302
scientific article