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.
Citation
Ronaldo Garcia. Carlos Gutierrez. Jorge Sotomayor. "Lines of principal curvature around umbilics and Whitney umbrellas." Tohoku Math. J. (2) 52 (2) 163 - 172, 2000. https://doi.org/10.2748/tmj/1178224605
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