Vol. 12, No. 1, 2019

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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
Abstract

We determine the lengths of all closed sub-Riemannian geodesics on the three-sphere S3 . Our methods are elementary and allow us to avoid using explicit formulas for the sub-Riemannian geodesics.

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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