Geodesic
Homogeneous variational problems and Lagrangian sections
Communications in Mathematics, Tome 24 (2016) no. 2, pp. 115-123 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53C22, 53C60
Keywords: Finsler geometry; line bundle; geodesics 
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     author = {Saunders, D.J.},
     title = {Homogeneous variational problems and {Lagrangian} sections},
     journal = {Communications in Mathematics},
     pages = {115--123},
     year = {2016},
     volume = {24},
     number = {2},
     mrnumber = {3590209},
     zbl = {1360.53077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2016_24_2_a2/}
}
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Saunders, D.J. Homogeneous variational problems and Lagrangian sections. Communications in Mathematics, Tome 24 (2016) no. 2, pp. 115-123. http://geodesic.mathdoc.fr/item/COMIM_2016_24_2_a2/

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