Homogeneous variational problems and Lagrangian sections
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 h...
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| Format: | Article |
| Language: | English |
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Sciendo
2016-12-01
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| Series: | Communications in Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/cm.2016.24.issue-2/cm-2016-0008/cm-2016-0008.xml?format=INT |
| 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. |
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| ISSN: | 2336-1298 |