$h$-Principles for curves and knots of constant torsion

Mohammad Ghomi; Matteo Raffaelli

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arXiv · 2410.06027

$h$-Principles for curves and knots of constant torsion

Mohammad Ghomi·Matteo Raffaelli

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Abstract

We prove that curves of constant torsion satisfy the $C^1$-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.

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Mohammad Ghomi, Matteo Raffaelli. 2024-10-08. $h$-Principles for curves and knots of constant torsion. https://arxiv.org/abs/2410.06027

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