Horocyclic evolutes, parallels and involutes of spacelike frontals in hyperbolic 2-space
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918477328023552 |
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| author | Nakatsuyama, Nozomi Takahashi, Masatomo Zhou, Anjie |
| author_facet | Nakatsuyama, Nozomi Takahashi, Masatomo Zhou, Anjie |
| contents | The horocyclic evolutes of spacelike frontals in hyperbolic 2-space have already been defined. Using enveloid theorem, we now define the horocyclic parallel and involute of a spacelike frontal in hyperbolic 2-space as the normal envelopes of its normal and tangent horocycles, respectively. Meanwhile, we investigate the relations among horocyclic evolutes, parallels and involutes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Horocyclic evolutes, parallels and involutes of spacelike frontals in hyperbolic 2-space Nakatsuyama, Nozomi Takahashi, Masatomo Zhou, Anjie Differential Geometry 53B30, 53C50, 57R45, 58K05 The horocyclic evolutes of spacelike frontals in hyperbolic 2-space have already been defined. Using enveloid theorem, we now define the horocyclic parallel and involute of a spacelike frontal in hyperbolic 2-space as the normal envelopes of its normal and tangent horocycles, respectively. Meanwhile, we investigate the relations among horocyclic evolutes, parallels and involutes. |
| title | Horocyclic evolutes, parallels and involutes of spacelike frontals in hyperbolic 2-space |
| topic | Differential Geometry 53B30, 53C50, 57R45, 58K05 |
| url | https://arxiv.org/abs/2605.00525 |