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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	363-376
Nombre de pages	14
journal	Bulletin of the Brazilian Mathematical Society
Volume	35
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s00574-004-0019-6
état	Publié - 1 nov. 2004
Modification externe	Oui

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10.1007/s00574-004-0019-6

Contient cette citation

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title = "Immersions with fractal set of points of zero Gauss-Kronecker curvature",

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

U2 - 10.1007/s00574-004-0019-6

DO - 10.1007/s00574-004-0019-6

M3 - Article

AN - SCOPUS:12444295547

SN - 1678-7544

VL - 35

SP - 363

EP - 376

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

IS - 3

ER -

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

Résumé

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