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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.
MSC:
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C22 Geodesics in global differential geometry
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