Differential geometry of curves in dual space
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916499286917120 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in the theory of dual curves, proving that there is a dual curve with prescribed curvature and torsion. Finally we classify all dual curves with constant curvature and torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential geometry of curves in dual space López, Rafael Differential Geometry Primary 53A10, Secondary 53C21, 53C42 We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in the theory of dual curves, proving that there is a dual curve with prescribed curvature and torsion. Finally we classify all dual curves with constant curvature and torsion. |
| title | Differential geometry of curves in dual space |
| topic | Differential Geometry Primary 53A10, Secondary 53C21, 53C42 |
| url | https://arxiv.org/abs/2411.19494 |