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Homogeneous variational problems and Lagrangian sections. (English) Zbl 1360.53077
Summary: We define a canonical line bundle over the slit tangent bundle of a manifold, and define a Lagrangian section to be a homogeneous section of this line bundle. When a regularity condition is satisfied the Lagrangian section gives rise to local Finsler functions. For each such section we demonstrate how to construct a canonically parametrized family of geodesics, such that the geodesics of the local Finsler functions are reparametrizations.
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C22 Geodesics in global differential geometry
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