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

Alexander Arbieto; Carlos Matheus

doi:10.1007/s00574-004-0019-6

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

Alexander Arbieto
, Carlos Matheus

IMPA

Research output: Contribution to journal › Article › peer-review

Abstract

We construct, for any "good" Cantor set F of S^n-1, an immersion of the sphere Sⁿ with set of points of zero Gauss-Kronecker curvature equal to F x D¹, where D¹ 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.

Original language	English
Pages (from-to)	363-376
Number of pages	14
Journal	Bulletin of the Brazilian Mathematical Society
Volume	35
Issue number	3
DOIs	https://doi.org/10.1007/s00574-004-0019-6
Publication status	Published - 1 Nov 2004
Externally published	Yes

Keywords

Cantor sets
Finite geometrical type
Immersions

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10.1007/s00574-004-0019-6

Cite this

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abstract = "We construct, for any {"}good{"} Cantor set F of Sn-1, an immersion of the sphere Sn with set of points of zero Gauss-Kronecker curvature equal to F x D1, where D1 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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AU - Matheus, Carlos

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N2 - We construct, for any "good" Cantor set F of Sn-1, an immersion of the sphere Sn with set of points of zero Gauss-Kronecker curvature equal to F x D1, where D1 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.

AB - We construct, for any "good" Cantor set F of Sn-1, an immersion of the sphere Sn with set of points of zero Gauss-Kronecker curvature equal to F x D1, where D1 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.

KW - Cantor sets

KW - Finite geometrical type

KW - Immersions

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DO - 10.1007/s00574-004-0019-6

M3 - Article

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EP - 376

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

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ER -

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

Abstract

Keywords

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