On the curvature of circles and curves in \(\mathbb{H}^n\) (Q2725248)
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scientific article; zbMATH DE number 1619035
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the curvature of circles and curves in \(\mathbb{H}^n\) |
scientific article; zbMATH DE number 1619035 |
Statements
12 July 2001
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osculating circles
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curvature of smooth curves
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Poincaré-model
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hyperbolic space
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Euclidean circles
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On the curvature of circles and curves in \(\mathbb{H}^n\) (English)
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The author computes the curvature of smooth curves in the Poincaré-model of the hyperbolic space \(\mathbb{H}^n_a\) (with constant curvature \(-a^2)\), and applies it to arcs of Euclidean circles in \(\mathbb{H}^n_ a\). Osculating circles are used to prove that any closed curve in \(\mathbb{H}^n_a\) carries at least one point, where the curvature is greater than \(a\).
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