Compact Liouville surfaces (Q1179724)
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scientific article; zbMATH DE number 25273
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compact Liouville surfaces |
scientific article; zbMATH DE number 25273 |
Statements
Compact Liouville surfaces (English)
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27 June 1992
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The generalized notion of a compact Liouville surface \((S,g,F)\) is introduced. The problem of the classification of such surfaces is studied. One of the main results is, that there is no Liouville metric, when the genus of \(S\) is greater than one. Some interesting geometrical applications are obtained. For example, the author finds examples of \(C_ \ell\) metrics on the two-dimensional sphere \(S^ 2\) different from Zoll's examples.
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geodesic flow
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Zoll's metric
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Liouville metric
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