Immersions with fractal set of points of zero Gauss-Kronecker curvature

Carlos Matheus | Arbieto, Alexander

Keywords: Immersions | Cantor sets | finite geometrical type

We construct, for any ``good'' Cantor set $F$ of $S^{n-1}$, an immersion of the sphere $S^n$ with set of points of zero Gauss-Kronecker curvature equal to $F\times D^{1}$, where $D^{1}$ is the $1$-dimensional disk. In particular these examples show that the theorem of Matheus-Oliveira strictly extends two results by do Carmo-Elbert and Barbosa-Fukuoka-Mercuri.

Anexos:

• imersoes.pdf