Closed Constant Curvature Space Curves

TL;DR

This paper presents a method for constructing closed space curves with constant curvature using differential equations and symmetry, applied to cylinders, tori, and via Frenet-Serret equations.

Contribution

It introduces a systematic approach to generate closed constant curvature curves on various surfaces using ODEs and symmetry considerations.

Findings

Successfully constructed closed constant curvature curves on cylinders and tori.

Demonstrated the use of Frenet-Serret equations for curve construction.

Provided a framework for analyzing symmetry in space curves.

Abstract

We use ODEs and symmetry arguments to construct closed constant curvature space curves, first on cylinders, next on tori, at last with the Frenet-Serret equations.