On analogs of the Reiss relation for curves on rational ruled surfaces (Q1822360)
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scientific article; zbMATH DE number 4002943
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On analogs of the Reiss relation for curves on rational ruled surfaces |
scientific article; zbMATH DE number 4002943 |
Statements
On analogs of the Reiss relation for curves on rational ruled surfaces (English)
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1985
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Let an algebraic curve C of degree d in \(P^ 2(R)\) intersect a line \(\ell\) in d distinct points \(P_ i(\ell)\); \(\kappa_ i(\ell)\) be the curvature of C at \(P_ i(\ell)\), \(\theta_ i(\ell)\) be the angle from \(\ell\) to C at \(P_ i(\ell)\). Then \(\sum^{d}_{i=1}(\kappa_ i(\ell)/\sin^ 3\theta_ i(\ell)) = 0\) (Reiss relation). The author obtains a number of interesting analogs of this relation.
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rational ruled surfaces
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algebraic curve
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curvature
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Reiss relation
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