On closed twisted curves

Rodrigues Costa, Sueli I.

doi:10.1090/S0002-9939-1990-0993746-1

On closed twisted curves
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by Sueli I. Rodrigues Costa PDF

Proc. Amer. Math. Soc. 109 (1990), 205-214 Request permission

Abstract:

Twisted curves in ${{\mathbf {R}}^m}$ are those which have independent derivatives up to order $m$. For plane and spatial curves the twisted condition is equivalent to never vanishing curvature and torsion respectively. We give a necessary and sufficient condition for a $(q,p)$-curve on a torus to be twisted, and use those curves to construct closed twisted curves in ${{\mathbf {R}}^m}$ for all $m$.

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