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

Alexander Arbieto·Carlos Matheus
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Abstract

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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Alexander Arbieto, Carlos Matheus. 2003-04-11. Immersions with fractal set of points of zero Gauss-Kronecker curvature. https://arxiv.org/abs/math/0304153

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