Approximations of Singular Surfaces with Standard Cuspidal Edges-Reference-Cited by-同舟云学术

Approximations of Singular Surfaces with Standard Cuspidal Edges

Published:2024-04-15 Issue:1 Volume:61 Page:16-29
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:SScMath

Author:

Saji Kentaro¹,Yamamoto Yoshiki¹²

Affiliation:

1. Department of Mathematics, Graduate School of Science, Kobe University, Rokkodai 1-1, Nada, Kobe 657-8501, Japan

2. OMRON Social Solutions Co. Ltd

Abstract

We consider a function from the Euclidean three space whose zero set is the image of the standard cuspidal edge. The composition of a parametrized singular surface in the three space with this function provides an approximation of the surface by the standard cuspidal edge. Taking a look at singularities of this composition, we study various approximations of singular surfaces like the cross cap, the generalized cuspidal edge and the swallowtail by standard cuspidal edges.

Publisher

Akademiai Kiado Zrt.

Link

https://akjournals.com/downloadpdf/journals/012/61/1/article-p16.xml

Reference28 articles.

1. [1]V. I. Arnold. Normal forms of functions near degenerate critical points, the Weyl groups , , and Lagrangian singularities. Funkcional. Anal. Prilozen., 6(4), 3-25:1972.

2. [2]V. I. Arnol'd, V. V. Goryunov, O. V. Lyashko and V. A. Vasil'ev. Singularity theory I. Encyclopaedia Math. Sci. 6, Springer-Verlag Berlin, 1993.

3. [3]V. I. Arnol'd, S. M. Gusein-Zade and A. N. Varchenko. Singularities of differentiable maps, Vol. 1. Monogr. Math., 82, Birkhäuser Boston, Inc., Boston, MA, 1985.

4. [4]M. Barajas S. and Y. Kabata. Projection of crosscap. Int. J. Geom. Methods Mod. Phys., 16(9):1950130, 2019.

5. [5]J. W. Bruce. Geometry of singular sets. Math. Proc. Cambridge Philos. Soc., 106(3):495-509, 1989.