Singularities of parallel surfaces

Details Singularities of parallel surfaces Singularities of parallel surfaces

2012-03-16

arxiv.org/abs/1203.3715v1

Mathematics

Differential Geometry

24 pages, final version, to appear in Tohoku Mathematical Journal

Scientific paper

We investigate singularities of all parallel surfaces to a given regular
surface. In generic context, the types of singularities of parallel surfaces
are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal
butterfly and 3-dimensional $D_4^\pm$ singularities. We give criteria for these
singularities types in terms of differential geometry (Theorem 3.4 and 3.5).

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