Knots of Constant Curvature

2004/03/04 by Jenelle Marie McAtee, McAtee, Jenelle Marie · 1 citation
Mathematics · Medicine · #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #Medical and Biological Sciences #math.GT #msc:57M99

paper · pdf · doi:10.48550/arxiv.math/0403089

arxiv created 2004/03/04 · openalex publication_date 2004/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show how to realize all knot (and link) types as C² smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "building blocks" that are particular segments of helices and circles. We use these building blocks to construct all closed braids.

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• h-Principles for smooth curves and knots with prescribed curvature

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