$h$-Principles for curves and knots of constant torsion
Abstract
We prove that curves of constant torsion satisfy the \mathcal{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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Numerical Analysis Techniques
Mathematics and Applications
Publication details
- Journal / source
- Commentarii Mathematici Helvetici
- Publication date
- 4 May 2026
- Language
- EN