Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Closed curves of constant torsion. II

Author: Joel L. Weiner
Journal: Proc. Amer. Math. Soc. 67 (1977), 306-308
MSC: Primary 53C40
MathSciNet review: 0461385
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C40

Retrieve articles in all journals with MSC: 53C40

Additional Information

Keywords: Closed space curves, constant torsion, total torsion, binormal indicatrix, Peano direction
Article copyright: © Copyright 1977 American Mathematical Society