Lines of principal curvature around umbilics and whitney umbrellas

Resumo

In this paper is studied the configuration of lines of curvature near a Whitney 3 umbrella which is the unique stable singularity for maps of surfaces into R . 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-Poincare characteristic in terms of the number of umbilics and umbrellas.

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Citação

GARCIA, Ronaldo; GUTIERREZ, Carlos ; SOTOMAYOR, Jorge. Lines of principal curvature around umbilics and whitney umbrellas. Tohoku Mathematical Journal, Sendai, v. 52, n. 2, p. 163-172, 2000.