Tohoku Mathematical Journal

Lines of principal curvature around umbilics and Whitney umbrellas

Ronaldo Garcia, Carlos Gutierrez, and Jorge Sotomayor

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Abstract

In this paper is studied the configuration of lines of curvature near a Whitney umbrella which is the unique stable singularity for maps of surfaces into $R^3$. The pattern of such configuration is established and characterized in terms of the 3-jet of the map. The result is used to establish an expression for the Euler-Poincaré characteristic in terms of the number of umbilics and umbrellas.

Article information

Source
Tohoku Math. J. (2), Volume 52, Number 2 (2000), 163-172.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178224605

Digital Object Identifier
doi:10.2748/tmj/1178224605

Mathematical Reviews number (MathSciNet)
MR1756092

Zentralblatt MATH identifier
0973.37012

Subjects
Primary: 58K15: Topological properties of mappings
Secondary: 53A05: Surfaces in Euclidean space

Keywords
Whitney umbrella singularity lines of curvature principal configuration

Citation

Garcia, Ronaldo; Gutierrez, Carlos; Sotomayor, Jorge. Lines of principal curvature around umbilics and Whitney umbrellas. Tohoku Math. J. (2) 52 (2000), no. 2, 163--172. doi:10.2748/tmj/1178224605. https://projecteuclid.org/euclid.tmj/1178224605


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References

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