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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.

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

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