@article{82e9c2b960a84b0d810058da59b6caf0,
title = "Curves of constant curvature and torsion in the 3-sphere",
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.",
keywords = "3-sphere, Frenet–Serret equations, constant curvature and torsion, curves in the 3-sphere, geodesic curvature, helix",
author = "Debraj Chakrabarti and Rahul Sahay and Jared Williams",
note = "Funding Information: MSC2010: 53A35. Keywords: Frenet–Serret equations, constant curvature and torsion, geodesic curvature, helix, 3-sphere, curves in the 3-sphere. All three authors were partially supported by a grant from the NSF (#1600371). Chakrabarti was partially supported by a grant from the Simons Foundation (#316632) and also by an Early Career internal grant from Central Michigan University. Publisher Copyright: {\textcopyright} 2019, Mathematical Sciences Publishers. All rights reserved.",
year = "2019",
doi = "10.2140/involve.2019.12.235",
language = "English",
volume = "12",
pages = "235--255",
journal = "Involve",
issn = "1944-4176",
publisher = "Involve",
number = "2",
}