A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913789336616960 |
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| author | Paul, Stepan |
| author_facet | Paul, Stepan |
| contents | We present numerical polyhedron data for the image of a piecewise-linear map from a zero-curvature Klein bottle into Euclidean 3-space such that every point in the domain has a neighborhood which is isometrically embedded. To the author's knowledge, this is the first explicit piecewise-smooth isometric immersion of a flat Klein bottle. Intuitively, the surface can be locally made from origami and but for the self-intersections has the global topology of a Klein bottle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space Paul, Stepan Geometric Topology Differential Geometry 52B99 We present numerical polyhedron data for the image of a piecewise-linear map from a zero-curvature Klein bottle into Euclidean 3-space such that every point in the domain has a neighborhood which is isometrically embedded. To the author's knowledge, this is the first explicit piecewise-smooth isometric immersion of a flat Klein bottle. Intuitively, the surface can be locally made from origami and but for the self-intersections has the global topology of a Klein bottle. |
| title | A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space |
| topic | Geometric Topology Differential Geometry 52B99 |
| url | https://arxiv.org/abs/2504.08826 |