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TOPOLOGICAL RIGIDITY FOR CERTAIN FAMILIES OF DIFFERENTIABLE PLANE CURVES

Published online by Cambridge University Press:  06 March 2002

JEAN PAUL DUFOUR  and
YASUHIRO KUROKAWA
JEAN PAUL DUFOUR
Affiliation:
Getodim Institut de Mathématiques, Université de Montpellier II, Place E Bataillon, 34060 Montpellier Cedex, France; dufourj@darboux.math.univmontp2.fr
YASUHIRO KUROKAWA
Affiliation:
Kita-ku Kita 37, Nishi 3, 1–25, Sapporo 001-0037, Japan; y-kurokw@math.sci.hokudai.ac.jp
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Abstract

It is shown that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case (that is, the double local case). The normal form of transversely joined two families of plane curves with second-order contact at the envelope is also given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 223 - 242
Copyright
2002 London Mathematical Society

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