All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions (Q923377)
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scientific article; zbMATH DE number 4169571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions |
scientific article; zbMATH DE number 4169571 |
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All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions (English)
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1991
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All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) are described explicitly. Final formulae for immersions in terms of theta- functions are obtained with the help of the finite-gap solutions and the Baker-Akhiezer function of the elliptic sinh-Gordon equation. A formula for the areas of the tori is presented.
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constant mean curvature
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theta-functions
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Baker-Akhiezer function
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sinh- Gordon equation
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areas
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tori
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