A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space
A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space
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.
Stepan Paul
数学
Stepan Paul.A piecewise-linear isometrically immersed flat Klein bottle in Euclidean 3-space[EB/OL].(2025-04-09)[2025-05-02].https://arxiv.org/abs/2504.08826.点此复制
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