Bertrand lightcone framed curves in the Lorentz-Minkowski 3-space
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913611558944768 |
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| author | Nakatsuyama, Nozomi Takahashi, Masatomo |
| author_facet | Nakatsuyama, Nozomi Takahashi, Masatomo |
| contents | We consider mixed types of not only regular curves but also curves with singular points in the Lorentz-Minkowski 3-space. In order to consider mixed type of curves with singular points, we consider the lightcone frame and lightcone framed curves. By using lightcone frame, we can consider Bertrand types for lightcone framed curves, so-called Bertrand lightcone framed curves. We clarify that the existence conditions of Bertrand lightcone framed curves in all cases. As a consequence, we find pseudo-circular involutes and evolutes of mixed type curves which appear as Bertrand lightcone framed curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bertrand lightcone framed curves in the Lorentz-Minkowski 3-space Nakatsuyama, Nozomi Takahashi, Masatomo Differential Geometry 53A35, 53C50, 58K05 We consider mixed types of not only regular curves but also curves with singular points in the Lorentz-Minkowski 3-space. In order to consider mixed type of curves with singular points, we consider the lightcone frame and lightcone framed curves. By using lightcone frame, we can consider Bertrand types for lightcone framed curves, so-called Bertrand lightcone framed curves. We clarify that the existence conditions of Bertrand lightcone framed curves in all cases. As a consequence, we find pseudo-circular involutes and evolutes of mixed type curves which appear as Bertrand lightcone framed curves. |
| title | Bertrand lightcone framed curves in the Lorentz-Minkowski 3-space |
| topic | Differential Geometry 53A35, 53C50, 58K05 |
| url | https://arxiv.org/abs/2412.10708 |