Translator Disclaimer
2019 Curves of constant curvature and torsion in the 3-sphere
Debraj Chakrabarti, Rahul Sahay, Jared Williams
Involve 12(2): 235-255 (2019). 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.

Citation

Download Citation

Debraj Chakrabarti. Rahul Sahay. Jared Williams. "Curves of constant curvature and torsion in the 3-sphere." Involve 12 (2) 235 - 255, 2019. https://doi.org/10.2140/involve.2019.12.235

Information

Received: 23 June 2017; Revised: 13 October 2017; Accepted: 22 April 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06980500
MathSciNet: MR3864216
Digital Object Identifier: 10.2140/involve.2019.12.235

Subjects:
Primary: 53A35

Keywords: 3-sphere , constant curvature and torsion , curves in the 3-sphere , Frenet–Serret equations , geodesic curvature , helix

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 2 • 2019
MSP
Back to Top