Vol. 12, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
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.

PDF Access Denied

We have not been able to recognize your IP address 3.137.185.180 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

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