The length spectrum of the sub-Riemannian three-sphere

Klapheck, David; VanValkenburgh, Michael

doi:10.2140/involve.2019.12.45

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The length spectrum of the sub-Riemannian three-sphere

David Klapheck and Michael VanValkenburgh

Vol. 12 (2019), No. 1, 45–61

DOI: 10.2140/involve.2019.12.45

Abstract

We determine the lengths of all closed sub-Riemannian geodesics on the three-sphere $S^{3}$ . Our methods are elementary and allow us to avoid using explicit formulas for the sub-Riemannian geodesics.

Keywords

sub-Riemannian geometry

Mathematical Subject Classification 2010

Primary: 53C17

Milestones

Received: 24 March 2017

Accepted: 6 March 2018

Published: 31 May 2018

Communicated by Kenneth S. Berenhaut

Authors

David Klapheck
Department of Mathematics and Statistics California State University, Sacramento Sacramento, CA United States

Michael VanValkenburgh
Department of Mathematics and Statistics California State University, Sacramento Sacramento, CA United States

Vol. 12, No. 1, 2019