The theorem of Fáry and Milnor for Hadamard manifolds (Q1392734)
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scientific article; zbMATH DE number 1180667
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The theorem of Fáry and Milnor for Hadamard manifolds |
scientific article; zbMATH DE number 1180667 |
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The theorem of Fáry and Milnor for Hadamard manifolds (English)
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8 October 1999
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The author shows that the total curvature of a knotted curve lying in a 3-dimensional Hadamard manifold is greater or equal to \(4\phi \). In the proof, he adapts to Hadamard manifolds the work by \textit{E. Pannwitz} [Math. Ann. 108, 629-672 (1933; Zbl 0007.23104)] for a knotted curve in Euclidean space \(E^n\).
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Hadamard manifold
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total curvature
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knotted curve
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