On closed twisted curves
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- by Sueli I. Rodrigues Costa
- Proc. Amer. Math. Soc. 109 (1990), 205-214
- DOI: https://doi.org/10.1090/S0002-9939-1990-0993746-1
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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 $m$.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 205-214
- MSC: Primary 53C75; Secondary 51L15, 53A04, 57R99
- DOI: https://doi.org/10.1090/S0002-9939-1990-0993746-1
- MathSciNet review: 993746