Invariant metrics and distances on generalized Neil parabolas (Q2469305)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant metrics and distances on generalized Neil parabolas |
scientific article |
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Invariant metrics and distances on generalized Neil parabolas (English)
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5 February 2008
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In this paper the authors give explicit formulas for the Carathéodory (inner and not inner) distance and metric, and for the Kobayashi distance and metric, of the Neil parabolas \(A_{n,m}=\{(z,w)\in\Delta^2\mid z^m=w^n\}\), where \(\Delta\) is the unit disk in the complex plane, and \(m< n\) are relatively prime natural numbers. The case \(m=2\) and \(n=3\) had been studied by \textit{G. Knese} [Mich. Math. J. 55, 139--154 (2007; Zbl 1131.32006)].
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Carathéodory distance
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Carathéodory metric
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Kobayashi distance
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Kobayashi metric
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Neil parabola
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