Lines of principal curvature around umbilics and Whitney umbrellas

Authors
Garcia, R Gutierrez, C Sotomayor, J
Citation
R. Garcia et al., Lines of principal curvature around umbilics and Whitney umbrellas, TOHOKU MATH, 52(2), 2000, pp. 163-172
Citations number
15
Categorie Soggetti
Mathematics
Journal title
TOHOKU MATHEMATICAL JOURNAL
ISSN journal
00408735 → ACNP
Volume
52
Issue
2
Year of publication
2000
Pages
163 - 172
Database
ISI
SICI code
0040-8735(200006)52:2<163:LOPCAU>2.0.ZU;2-Y
Abstract
In this paper is studied the configuration of lines of curvature near a Whi tney umbrella which is the unique stable singularity for maps of surfaces i nto 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 expre ssion for the Euler-Poincare characteristic in terms of the number of umbil ics and umbrellas.