An Explicit Formula for the Spherical Curves with Constant Torsion

Demetre Kazaras; Ivan Sterling

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arXiv · 1312.0140

An Explicit Formula for the Spherical Curves with Constant Torsion

Demetre Kazaras·Ivan Sterling

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Abstract

The purpose of this article is to give an explicit formula for all curves of constant torsion $τ$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are discussed in the Appendix. Some example curves, computed with a standard ODE package, with $τ=.1,.5,1,2$ are shown in Figure \ref{peter}. Though their existence and some of their general properties were known, our explicit formulas for them, in terms of hypergeometric functions, are new.

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Demetre Kazaras, Ivan Sterling. 2013-11-30. An Explicit Formula for the Spherical Curves with Constant Torsion. https://arxiv.org/abs/1312.0140

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