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.
Publié le : 2000-05-14
Classification:
Whitney umbrella singularity,
lines of curvature,
principal configuration,
58K15,
53A05
@article{1178224605,
author = {Garcia, Ronaldo and Gutierrez, Carlos and Sotomayor, Jorge},
title = {Lines of principal curvature around umbilics and Whitney umbrellas},
journal = {Tohoku Math. J. (2)},
volume = {52},
number = {4},
year = {2000},
pages = { 163-172},
language = {en},
url = {http://dml.mathdoc.fr/item/1178224605}
}
Garcia, Ronaldo; Gutierrez, Carlos; Sotomayor, Jorge. Lines of principal curvature around umbilics and Whitney umbrellas. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp. 163-172. http://gdmltest.u-ga.fr/item/1178224605/