Dressing curves

TL;DR

This paper introduces a loop group framework for analyzing curves in three-dimensional space and uses it to classify special curves called circletons, which are obtained by dressing circles with simple factors.

Contribution

It provides a novel loop group approach to curve classification and introduces the concept of circletons as dressed circles.

Findings

Loop group description for curves in R^3

Classification of circletons via dressing transformations

New insights into curve transformations in differential geometry

Abstract

We present a loop group description for curves in $\mathbb{R}^3$, and apply it to classify the circletons: Circles dressed by simple factors.