Preprint A204/2003
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.