Geodesic flows on diffeomorphism groups with Sobolev metrics and integrable systems (Q1850872)
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scientific article; zbMATH DE number 1845289
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geodesic flows on diffeomorphism groups with Sobolev metrics and integrable systems |
scientific article; zbMATH DE number 1845289 |
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Geodesic flows on diffeomorphism groups with Sobolev metrics and integrable systems (English)
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15 December 2002
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It is well-known that the hydrodynamics on an incompressible ideal fluid can be described by the geodesic flow on the group of volume preserving transformations with respect to a certain right invariant metric. In this paper the author shows that the supersymmetric Harry-Dym equation can be also described by geodesic motions on the Bott-Virasoro group, which is an extension of the group of diffeomorphisms on the circle.
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hydrodynamics
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geodesic flows on diffeomorphism groups
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