Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917116072951808 |
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| author | Fukunaga, Tomonori Nakatsuyama, Nozomi Takahashi, Masatomo |
| author_facet | Fukunaga, Tomonori Nakatsuyama, Nozomi Takahashi, Masatomo |
| contents | We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the theories of generalised framed surfaces and framed surfaces. We introduce the notion of translation generalised framed surfaces and investigate types of singular points that appear on translation generalised framed base surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space Fukunaga, Tomonori Nakatsuyama, Nozomi Takahashi, Masatomo Differential Geometry Geometric Topology 58K05, 57R45, 53A05 We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the theories of generalised framed surfaces and framed surfaces. We introduce the notion of translation generalised framed surfaces and investigate types of singular points that appear on translation generalised framed base surfaces. |
| title | Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space |
| topic | Differential Geometry Geometric Topology 58K05, 57R45, 53A05 |
| url | https://arxiv.org/abs/2512.01347 |