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Generic isotopies of space curves

Published online by Cambridge University Press:  18 May 2009

J. W. Bruce  and
P. J. Giblin
J. W. Bruce
Affiliation:
Department of Mathematics, The University Newcastle-upon-Tyne, NE17RUEngland
P. J. Giblin
Affiliation:
Department of Pure Mathematics, The University Liverpool, L69 3BXEngland
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For a single space curve (that is, a smooth curve embedded in ℝ3) much geometrical information is contained in the dual and the focal set of the curve. These are both (singular) surfaces in ℝ3, the dual being a model of the set of all tangent planes to the curve, and the focal set being the locus of centres of spheres having at least 3-point contact with the curve. The local structures of the dual and the focal set are (for a generic curve) determined by viewing them as (respectively) the discriminant of a family derived from the height functions on the curve, and the bifurcation set of the family of distance-squared functions on the curve. For details of this see for example [6, pp. 123–8].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 41 - 63
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

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