|
|||||
 |
|
|
|
|
|
|
|
Curves of
constant curvature and torsion in the 3-sphere
Debraj Chakrabarti, Rahul Sahay and Jared Williams
Vol. 12 (2019), No. 2, 235–255
DOI: 10.2140/involve.2019.12.235
|
Abstract |
|
We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global behavior may be periodic or the curve may be dense in a Clifford torus embedded in the 3-sphere. This behavior is very different from that of helices in three-dimensional Euclidean space, which also have constant curvature and torsion. |
PDF Access Denied
However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve
We have not been able to recognize your IP address
34.234.207.100
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
Frenet–Serret equations, constant curvature and torsion,
geodesic curvature, helix, 3-sphere, curves in the 3-sphere
|
Mathematical Subject Classification 2010
Primary: 53A35
|
Milestones
Received: 23 June 2017
Revised: 13 October 2017
Accepted: 22 April 2018
Published: 8 October 2018
Communicated by Colin Adams
|
Authors |
| Debraj Chakrabarti | |
| Department of Mathematics Central Michigan University Mt. Pleasant, MI United States |
|
| Rahul Sahay | |
| University of California Berkeley, CA United States |
|
| Jared Williams | |
| Department of Physics and
Astronomy University of Missouri Columbia, MO United States |
|
