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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2020.tde-27072020-180126
Document
Author
Full name
Maria Carolina Zanardo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Nabarro, Ana Claudia (President)
Dias, Fábio Scalco
Ruas, Maria Aparecida Soares
Silva, Jorge Luiz Deolindo
Title in Portuguese
Geometria local associada à aplicação de Gauss de hipersuperfícies em R4
Keywords in Portuguese
Aplicação de Gauss
Conjunto parabólico
Função altura
Hipersuperfície canal
Abstract in Portuguese
Esta tese é dedicada ao estudo das propriedades geométricas provenientes, principalmente, das singularidades da aplicação de Gauss e das singularidades da família de funções altura em uma hipersuperfície M em R4. Obtemos caracterizações geométricas de singularidades estáveis da aplicação de Gauss de M, ou seja, singularidades de codimensão menor ou igual a 3, usando singularidades multilocais da função altura em M. Além disso, relacionamos singularidades da função altura sobre M e singularidades da função altura sobre o conjunto parabólico de M, visto como uma superfície em R4. Também consideramos um caso particular: a hipersuperfície canal de uma curva em R4, para o qual os resultados são mais precisos e envolvem relações com as singularidades da família de funções altura sobre a curva.
Title in English
Local geometry associated with the Gauss map of hypersurfaces in R4
Keywords in English
Canal hypersurface
Gauss map
Height function
Parabolic set
Abstract in English
This thesis is dedicated to the study of geometric properties derived mostly from the singularities of the Gauss map and from the singularities of the family of height functions on a hyperfurface M in R4. We obtain geometric characterizations regarding stable singularities of the Gauss map of M, that is, singularities which codimension is less than or equal to 3, using multilocal singularities of the family of height functions on M. In addition, we analyse the relatation between the singularities of the height function on M and singularities of the height function on the parabolic set of M, seen as a surface in R4. We also consider a particular case: the canal hypersurface of a curve in R4, in which the results are more accurate and involve relations with the singularities of the family of height functions on the curve.
 
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Publishing Date
2020-07-27
 
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