## D. J. Saunders - Homogeneous variational problems and Lagrangian sections

cm:9454 - Communications in Mathematics, December 22, 2016, Volume 24 (2016), Issue 2 - https://doi.org/10.1515/cm-2016-0008
Homogeneous variational problems and Lagrangian sections

Authors: D. J. Saunders

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.

Volume: Volume 24 (2016), Issue 2
Published on: December 22, 2016
Imported on: May 11, 2022
Keywords: General Mathematics,[MATH]Mathematics [math]