English

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 D4±D_4^\pm singularities. We give criteria for these singularities types in terms of differential geometry (Theorem 3.4 and 3.5).

Keywords

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

R2 v1 2026-06-21T20:35:14.535Z