Tohoku Mathematical Journal

Singularities of parallel surfaces

Toshizumi Fukui and Masaru Hasegawa

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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).

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 3 (2012), 387-408.

Dates
First available in Project Euclid: 11 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1347369369

Digital Object Identifier
doi:10.2748/tmj/1347369369

Mathematical Reviews number (MathSciNet)
MR2979288

Zentralblatt MATH identifier
1257.53005

Subjects
Primary: 53A05: Surfaces in Euclidean space
Secondary: 58K05: Critical points of functions and mappings 58K35: Catastrophe theory

Keywords
Parallel surface Versality of distance squared functions

Citation

Fukui, Toshizumi; Hasegawa, Masaru. Singularities of parallel surfaces. Tohoku Math. J. (2) 64 (2012), no. 3, 387--408. doi:10.2748/tmj/1347369369. https://projecteuclid.org/euclid.tmj/1347369369


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