Cusp singularities of plane envelopes

Details Cusp singularities of plane envelopes Cusp singularities of plane envelopes

2005-11-21

arxiv.org/abs/math/0511511v1

Mathematics

Differential Geometry

13 pp; 3 figures

Scientific paper

We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the $\A$-normal form of these families, their envelopes and local patterns near the cusp. We obtain a new codimension 2 singularity of envelopes (two transversal semicubic cusps), and we describe its perestroikas under generic small deformations.

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