Geometry of curves passing through Whitney umbrella
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866908639346819072 |
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| author | Hayashi, Hiroyuki |
| author_facet | Hayashi, Hiroyuki |
| contents | We study geometry of curves passing through a Whitney umbrella by using a Darboux frame along it. We define three invariants by using Frenet-Serre type formula relating to the geodesic curvature, the normal curvature, and the geodesic torsion. We investigate the degrees of divergence and the top-terms of these invariants and their geometric meanings. We also consider a developable surface along the curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of curves passing through Whitney umbrella Hayashi, Hiroyuki Differential Geometry Geometric Topology We study geometry of curves passing through a Whitney umbrella by using a Darboux frame along it. We define three invariants by using Frenet-Serre type formula relating to the geodesic curvature, the normal curvature, and the geodesic torsion. We investigate the degrees of divergence and the top-terms of these invariants and their geometric meanings. We also consider a developable surface along the curve. |
| title | Geometry of curves passing through Whitney umbrella |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2410.00459 |