Deformations of swallowtails in a 3-dimensional space form
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913555633143808 |
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| author | Saji, Kentaro Umehara, Masaaki Yamada, Kotaro |
| author_facet | Saji, Kentaro Umehara, Masaaki Yamada, Kotaro |
| contents | This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we investigate map germs of generic swallowtails in 3-dimensional space from, and show some important properties of them. In particular, we give a representation formula giving all map germs of swallowtails in the Euclidean 3-space whose Gaussian curvatures are bounded from below by a positive constant or by a negative constant from above. Using this, we show that any swallowtails are deformed into a swallowtail of constant Gaussian curvature preserving the sign of their Gaussian curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of swallowtails in a 3-dimensional space form Saji, Kentaro Umehara, Masaaki Yamada, Kotaro Differential Geometry 53A10, 53A35 This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we investigate map germs of generic swallowtails in 3-dimensional space from, and show some important properties of them. In particular, we give a representation formula giving all map germs of swallowtails in the Euclidean 3-space whose Gaussian curvatures are bounded from below by a positive constant or by a negative constant from above. Using this, we show that any swallowtails are deformed into a swallowtail of constant Gaussian curvature preserving the sign of their Gaussian curvatures. |
| title | Deformations of swallowtails in a 3-dimensional space form |
| topic | Differential Geometry 53A10, 53A35 |
| url | https://arxiv.org/abs/2406.05971 |