2018-06-142018-06-142000GARCIA, 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, 2000.0040-8735e- 2186-585Xhttp://repositorio.bc.ufg.br/handle/ri/15248In 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.engAcesso AbertoArtigo