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

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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.
13 pages, 3 figures

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Differential Geometry, 53C42

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http://salesiana.dossiersoluciones.com/handle/123456789/67053

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304153
 http://arxiv.org/abs/math/0304153

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arXiv