2018-06-132018-06-132003GARCIA, Ronaldo; SOTOMAYOR, Jorge. A metric property of umbilic points. Anais da Academia Brasileira de Ciências, Rio de Janeiro, v. 75, n. 4, p. 405-413, 2003.0001-3765e- 1678-2690http://repositorio.bc.ufg.br/handle/ri/15237In the space of cubic forms of surfaces, regarded as a G-space and endowed with a natural invariant metric, the ratio of umbilic points with a negative index to those with a positive index is evaluated in terms of the asymmetry of the metric, defined here. This work contains also a section with references pertinent to umbilic points and one with a discussion of a connection of the above defined ratio with that reported in 1977 by Berry and Hannay in the domain of Statistical Physics.engAcesso AbertoUmbilic pointPrincipal curvature linesPonto umbílicoLinhas de curvaturas principaisArtigo10.1590/S0001-37652003000400001