We study the geometry of surfaces in R 3 with corank 1 singularities. At a singular point we define the curvature parabola using the first and second fundamental forms of the surface, which contains all the local second order geometrical information about the surface. The curvature parabola is used to introduce the concepts of asymptotic directions and umbilic curvature, which are related to contact properties of the surface with planes and spheres.

No abstract

No abstract

No abstract

We derive geometrical information on smooth surfaces in R 4 from the geometry of their images under linear projections to 3-spaces.