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Communications in Mathematics

Editor-in-Chief: Rossi, Olga

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Homogeneous variational problems and Lagrangian sections

D. J. Saunders
  • Corresponding author
  • Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czechia
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Published Online: 2016-12-22 | DOI: https://doi.org/10.1515/cm-2016-0008

Abstract

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.

Keywords: Finsler geometry; line bundle; geodesics

References

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About the article

Received: 2016-10-25

Accepted: 2016-12-04

Published Online: 2016-12-22

Published in Print: 2016-12-01


Citation Information: Communications in Mathematics, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2016-0008.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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