On the singularities of almost-simple plane curves (Q791911)
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scientific article; zbMATH DE number 3851978
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the singularities of almost-simple plane curves |
scientific article; zbMATH DE number 3851978 |
Statements
On the singularities of almost-simple plane curves (English)
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1983
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The author considers closed curves in the real projective plane which fulfill some regularity conditions formulated in terms of direct differential geometry. Let \(n_ 1\), \(n_ 2\), \(n_ 3\) be the number of inflection points, cusps, and beaks, respectively. The following theorem is proved: If C has even order and if each multiple point decomposes C into curves which are met by every line, then \(n_ 1+n_ 2+n_ 3\geq 2\) and \(n_ 1+2n_ 2+n_ 3\geq 4.\)
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plane curves
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inflection points
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cusps
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beaks
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