HOME > Table of Contents and Abstracts > Vol. 64, No. 3
Tohoku Mathematical Journal
SECOND SERIES VOL. 64, NO. 3
|Tohoku Math. J.|
64 (2012), 387-408
SINGULARITIES OF PARALLEL SURFACES
Toshizumi Fukui and Masaru Hasegawa
(Received September 6, 2010, revised December 28, 2011)
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).
2000 Mathematics Subject Classification.
Primary 53A05; Secondary 58K05, 58K35.
Key words and phrases.
Parallel surface, Versality of distance squared functions.
To the top of this page
Back to the Contents