Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Closed curves of constant torsion. II
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by Joel L. Weiner
Proc. Amer. Math. Soc. 67 (1977), 306-308
DOI: https://doi.org/10.1090/S0002-9939-1977-0461385-0

Abstract:

In this note we show that there exist closed regular ${C^3}$ space curves $\alpha$ with curvature $\kappa > 0$ and nonzero constant torsion $\tau$ whose total torsion $\smallint _\alpha {\tau \;ds}$ is arbitrarily small. In so doing, we give another proof of the existence of closed curves of nonzero constant torsion. This note shows that Conjecture 2 in [2] is incorrect since the preceding statement is equivalent to the statement that there exist closed curves of constant torsion $\tau = 1$ whose length is arbitrarily small.
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 67 (1977), 306-308
  • MSC: Primary 53C40
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0461385-0
  • MathSciNet review: 0461385