Open Access
2012 Singularities of parallel surfaces
Toshizumi Fukui, Masaru Hasegawa
Tohoku Math. J. (2) 64(3): 387-408 (2012). DOI: 10.2748/tmj/1347369369

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 $D_4^\pm$ singularities. We give criteria for these singularity types in terms of differential geometry (Theorems 3.4 and 3.5).

Citation

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Toshizumi Fukui. Masaru Hasegawa. "Singularities of parallel surfaces." Tohoku Math. J. (2) 64 (3) 387 - 408, 2012. https://doi.org/10.2748/tmj/1347369369

Information

Published: 2012
First available in Project Euclid: 11 September 2012

zbMATH: 1257.53005
MathSciNet: MR2979288
Digital Object Identifier: 10.2748/tmj/1347369369

Subjects:
Primary: 53A05
Secondary: 58K05 , 58K35

Keywords: parallel surface , Versality of distance squared functions

Rights: Copyright © 2012 Tohoku University

Vol.64 • No. 3 • 2012
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