Pedro Benedini Riul (ICMC-USP)

Thursday, August 24th, 10:20, Room 4-111

 Title: Singular surfaces in R4


This talk is divided in two parts. In the first one, we present a more general study about the geometry of surfaces in R4 with corank 1 singularities. At the singular point we define the curvature parabola using the first and second fundamental forms of the surface. This definition was inspired by the one made by
Martins and Nuño-Ballesteros (2015). As they did, we show that the curvature parabola contains all the local second order geometrical information of the surface. Also, the definitions and some results about asymptotic directions and umbilic curvature are given. The second part is dedicated to the flat geometry of the map germ f : (R2, 0) → (R4, 0) given by (x, y) 7→ (x, xy, y2, y3).