Vertices and inflexions of plane sections of surfaces in R

Abstract

We discuss the behaviour of vertices and inflexions of one-parameter families of plane curves which include a singular member. These arise a sectons of smooth surfaces by families of planes parallel to the tangent plane at a given point. We cover all the generic cases, namely elliptic, umbilic, hyperbolic, parabolic and cusp of Gauss points. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.

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Cite this paper

@inproceedings{Diatta2005VerticesAI, title={Vertices and inflexions of plane sections of surfaces in R}, author={Andr{\'e} Diatta and Peter J. Giblin}, year={2005} }