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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On closed twisted curves


Author: Sueli I. Rodrigues Costa
Journal: Proc. Amer. Math. Soc. 109 (1990), 205-214
MSC: Primary 53C75; Secondary 51L15, 53A04, 57R99
MathSciNet review: 993746
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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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0993746-1
PII: S 0002-9939(1990)0993746-1
Keywords: Nowhere vanishing torsion curves, four-vertex theorem, order $ n$ singularity
Article copyright: © Copyright 1990 American Mathematical Society