The Length Spectrum of the Sub-Riemannian Three-Sphere

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.

17 pages, 10 figures

References in corpus (1)

• Hopf fibration: geodesics and distances

Cited by in corpus (2)

• Length spectra of sub-Riemannian metrics on compact Lie groups
• Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case