Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space (Q1088035)
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scientific article; zbMATH DE number 3989776
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space |
scientific article; zbMATH DE number 3989776 |
Statements
Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space (English)
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1985
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Two theorems on relationship between the Liouville equation \((\partial^ 2/\partial z\partial \bar z)\phi =e^{\phi}\) and geometry of Teichmüller space are announced: (i) If \(\phi\) satisfies the Liouville equation, an explicitly defined integral S(\(\phi)\) is stated to be the generating function for accessory parameters on Teichmüller space. (ii) S is stated to be the potential of the Weil-Peterson metric on that space.
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Liouville equation
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Teichmüller space
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potential of the Weil-Peterson metric
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