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

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

2003-04-11

arxiv.org/abs/math/0304153v1

Mathematics

Differential Geometry

13 pages, 3 figures

Scientific paper

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.

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