Involve: A Journal of Mathematics
- Volume 12, Number 2 (2019), 235-255.
Curves of constant curvature and torsion in the 3-sphere
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.
Involve, Volume 12, Number 2 (2019), 235-255.
Received: 23 June 2017
Revised: 13 October 2017
Accepted: 22 April 2018
First available in Project Euclid: 25 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A35: Non-Euclidean differential geometry
Chakrabarti, Debraj; Sahay, Rahul; Williams, Jared. Curves of constant curvature and torsion in the 3-sphere. Involve 12 (2019), no. 2, 235--255. doi:10.2140/involve.2019.12.235. https://projecteuclid.org/euclid.involve/1540432914