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Bibliographic Details
Main Author: Paul, Stepan
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.08826
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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