$h$-Principles for curves and knots of constant torsion
Mohammad Ghomi, Matteo Raffaelli
Published: 2024/10/8
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.