  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.
