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.
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