Classifications of cusps appearing on plane curves
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909111561486336 |
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| author | Matsushita, Yoshiki |
| author_facet | Matsushita, Yoshiki |
| contents | In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for $(n, n+1)$ cusps with respect to several differential conditions and relations between these singularities and evolutes of fronts. We give complete classifications with respect to $(4, 5)$-cusps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifications of cusps appearing on plane curves Matsushita, Yoshiki Differential Geometry 58K40, 58K05, 58C27 In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for $(n, n+1)$ cusps with respect to several differential conditions and relations between these singularities and evolutes of fronts. We give complete classifications with respect to $(4, 5)$-cusps. |
| title | Classifications of cusps appearing on plane curves |
| topic | Differential Geometry 58K40, 58K05, 58C27 |
| url | https://arxiv.org/abs/2402.12166 |