The Length Spectrum of the Sub-Riemannian Three-Sphere

TL;DR

This paper characterizes all closed geodesics in the sub-Riemannian three-sphere, providing a comprehensive understanding of their length spectrum through elementary methods without explicit formulas.

Contribution

It offers a novel elementary approach to determine the length spectrum of closed geodesics on the sub-Riemannian three-sphere, avoiding explicit geodesic formulas.

Findings

Complete classification of closed sub-Riemannian geodesic lengths

Elementary methods simplify the analysis

Explicit length spectrum obtained

Abstract

We determine the lengths of all closed sub-Riemannian geodesics on the three-sphere. Our methods are elementary and allow us to avoid using explicit formulas for the sub-Riemannian geodesics.