Simple umbilics revisited
This paper deals with an old result of Cayley and Darboux concerning the topological classification of simple umbilical points of a smooth surface in \(E^3\), i.e. umbilical points which cannot be broken into simpler by a small deformation of the surface. The author proves among others the following stability theorem: The 3-jet of the germ at an isolated simple umbilical point is topologically sufficient. Furthermore, the configuration of the lines of principal curvature in the neighborhood of such an umbilical point belongs to exactly one of four classes called ``tripod'', ``sunset'', ``degenerate sunset'' and ``thorn''.
scientific article; zbMATH DE number 1567207