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On the tangent developable of a space curve

Published online by Cambridge University Press:  24 October 2008

David Mond
David Mond
Affiliation:
University of Liverpool
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Summary

In this paper we investigate the local form of the tangent developable of a curve in 3-space, and obtain results relating this to the order of vanishing of the torsion. In particular,

Theorem 1. If at the point γ(t) on the curve γ, the torsion vanishes to order k (0 ≼ k ≼ 4), then the germ of the tangent developable at that point has one curve of self intersection if k is odd, and none if k is even.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 351 - 355
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Cleave, J. P.The form of the tangent developable at points of zero torsion on space curves. Proc. Cambridge Philos. Soc. 88 (1980), 403–407.CrossRefGoogle Scholar
(2)Gaffney, T. Properties of finitely determined germs. Ph.D. thesis, Brandeis University, 1975.Google Scholar
(3)Gaffney, T.A note on the order of determination of a finitely determined germ. Invent. Math. 52 (1979), 127–135.CrossRefGoogle Scholar
(4)Gibson, C. G. Singular points of smooth mappings. Research notes in mathematics 25, Pitman, 1979.Google Scholar
(5)Martinet, J. Déploiements versel's des applications différentiables et classification des applications stables. Lecture Notes in Math. 535 (Springer), 1976, 1–44.Google Scholar
(6)Mond, D.The A-Classification of some map-germs from ℝ2 to ℝ3. Preprint, Liverpool University, 1981.Google Scholar
(7)Gaffney, T. and Du Plessis, A.More on the determinacy of smooth map-germs. Preprint Series 1980/81 No. 31, Matematisk Institut, Aarhus Universitet.CrossRefGoogle Scholar