• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2021.tde-21072021-164923
Document
Author
Full name
Marco Antônio do Couto Fernandes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2021
Supervisor
Committee
Tari, Farid (President)
Craizer, Marcos
Figueiredo Junior, Ruy Tojeiro de
Mello, Luis Fernando de Osório
Title in Portuguese
Pontos Umbílicos e Curvas Especiais em Superfícies no Espaço Minkowski
Keywords in Portuguese
Conjectura de carathéodory
Espaço Minkowski
Ponto umbílico
Superfície
Abstract in Portuguese
O estudo de superfícies no espaço Minkowski apresenta diferenças com relação ao caso Euclidiano. A mudança na primeira forma fundamental cria pontos onde a métrica pode se degenerar e pontos onde as direções principais coincidem. Tais conjunto são denotados por LD e LPL, respectivamente, e as suas singularidades dão origem aos pontos umbílicos. Este trabalho contêm um estudo a respeito da geometria diferencial de superfícies em R31 , abordando temas como as interseções entre o LD e o LPL, a multiplicidade de pontos umbílicos, deformações de fenômenos de codimensão 1 em famílias de superfícies a 1-parâmetro e a inversão de Möbius. Os resultados obtidos visam contribuir com uma possível generalização da Conjectura de Carathéodory no espaço Minkowski provada por Farid Tari.
Title in English
Umbilic Points and Special Curves on Surfaces in Minkowski Space
Keywords in English
Carathéodory conjecture
Minkowski space
Surface
Umbilic point
Abstract in English
The study of surfaces in the Minkowski 3-space presents differences in relation to the Euclidean 3- space. The induced metric can degenerate at some points and the principal directions can coincide at other points. These sets are denoted by LD and LPL, respectively, and their singularities give rise to umbilic points. This thesis contains a study on the differential geometry of surfaces in the Minkowski 3-space, addressing topics such as the intersections between the LD and the LPL, the multiplicity of umbilic points, deformations of codimension 1 phenomena in 1-parameter families of surfaces and the Möbius inversion. The results obtained are a contribution to a possible generalization of the Carathéodory Conjecture in Minkowski 3-space proved by Farid Tari.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Publishing Date
2021-07-21
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.