h-Principles for curves and knots of constant torsion

2024/10/08 by Mohammad Ghomi, Ghomi, Mohammad, Matteo Raffaelli +1 · 1 citation
#53C21 #57K10 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A04 #Secondary 58C35

paper · doi:10.48550/arxiv.2410.06027

Abstract

We prove that curves of constant torsion satisfy the C¹-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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• h-Principles for smooth curves and knots with prescribed curvature

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