Singularities of parallel surfaces
Differential Geometry
2012-03-19 v1
Abstract
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 singularities. We give criteria for these singularities types in terms of differential geometry (Theorem 3.4 and 3.5).
Cite
@article{arxiv.1203.3715,
title = {Singularities of parallel surfaces},
author = {Toshizumi Fukui and Masaru Hasegawa},
journal= {arXiv preprint arXiv:1203.3715},
year = {2012}
}
Comments
24 pages, final version, to appear in Tohoku Mathematical Journal