Geodesic flows on compact surfaces -- as an application of Hamiltonian formalism (Q2367577)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geodesic flows on compact surfaces -- as an application of Hamiltonian formalism |
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Geodesic flows on compact surfaces -- as an application of Hamiltonian formalism (English)
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19 September 1993
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The author derives the well known fact that the geodesic flow on a Riemannian manifold is just the Hamiltonian flow for the pointwise energy as Hamiltonian. Explicit equations for the geodesics on the two-torus \(T^ 2\) of rotation and the ellipsoid with three different major axes are given, and the closed geodesics on \(T^ 2\) are determined; all this is well known as well.
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geodesic flow
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Riemannian manifold
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Hamiltonian flow
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two-torus
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ellipsoid
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