Connections in -vector bundles.

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.

The inverse problem of the calculus of variations for Finsler structures

Demeter Krupka, Abdurasoul Èzbekhovich Sattarov (1985)

Mathematica Slovaca

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On Finsler connections.

Angel Montesinos (1979)

Revista Matemática Hispanoamericana

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A new definition for lifts and lowerings is given, linking the different tensor algebras involved in the usual treatment of Finsler manifolds. By means of them, the relation between the different classes of linear connections is made clearer.

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