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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

[en] REPRESENTATION OF GENERIC CURVES BY THEIR SINGULARITIES / [pt] REPRESENTAÇÃO DE CURVAS GENÉRICAS POR SUAS SINGULARIDADES

FILIPE BELLIO DA NOBREGA 08 January 2019 (has links)
[pt] O objetivo desta pesquisa é estudar as propriedades geométricas e topológicas de curvas genéricas imersas no plano. Neste caso ser genérica significa que a curva só pode ter pontos duplos sem tangentes comuns nas duas passagens. Pode-se nomear as n singularidades da curva usando símbolos como a1, ... , an. Percorrendo a curva, produz-se uma palavra cíclica de tamanho 2n. Entretanto, nem toda palavra está relacionada a uma curva plana, há requisitos sobre a sua combinatória, o primeiro dos quais foi descoberto por Gauss. Avanços foram realizados no estudo de curvas localmente convexas no plano, na esfera e no plano projetivo. / [en] The aim of this work is to study the topological and geometric properties of closed generic immersed curves in the plane. In this case, generic means that the curve can only have double points without a common tangent. One can label the singularities using n symbols, such as a1, ... , an. Going around the curve, a cyclic word of length 2n is produced. However, not every word is related to a planar curve, there are requirements on its combinatorics, the first of which was found by Gauss. Advances were made in the study of locally convex curves on the plane, the sphere and the projective plane.

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