$h$-Principles for curves and knots of constant torsion
Differential Geometry
2025-10-06 v2
Abstract
We prove that curves of constant torsion satisfy the -dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex integration and degree theory, quickly establish these results for curves of constant curvature as well.
Cite
@article{arxiv.2410.06027,
title = {$h$-Principles for curves and knots of constant torsion},
author = {Mohammad Ghomi and Matteo Raffaelli},
journal= {arXiv preprint arXiv:2410.06027},
year = {2025}
}
Comments
7 pages, 1 figure; Minor revisions; Accepted for publication in Comment. Math. Helv