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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2021.tde-22042021-184304
Document
Author
Full name
Bruna Vieira da Silva Flores
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2021
Supervisor
Committee
Chaves, Rosa Maria dos Santos Barreiro (President)
Camargo, Fernanda Ester Camillo
Santos, Eliane da Silva dos
Title in Portuguese
Representação de Enneper para superfícies mínimas nos espaços Euclidiano e de Lorentz-Minkowski
Keywords in Portuguese
Espaço de Lorentz-Minkowski
Espaço Euclidiano
Representação de Enneper
Superfícies mínimas
Abstract in Portuguese
Neste trabalho, estudamos as representações de tipo-Enneper para superfícies mínimas no espaço Euclidiano R3 e superfícies máximas no espaço de Lorentz-Minkowski L3, usando análise complexa, e estudamos uma representação de tipo-Enneper para superfícies mínimas tipo tempo em L3, usando análise para-complexa. Assim, nós introduzimos alguns resultados de análise complexa e para-complexa e os utilizamos para provar teoremas de representação de Weierstrass em R3 e L3. São exibidos alguns exemplos de superfícies mínimas em R3 e L3, construídas via fórmula de Representação de Enneper, que é equivalente à fórmula de representação de Weierstrass, obtidas para as mesmas superfícies.
Title in English
Enneper representation of minimal surfaces in the Euclidean and Lorentz-Minkowski spaces
Keywords in English
Enneper representation
Euclidean space
Lorentz-Minkowski space
Minimal surfaces
Abstract in English
In this work, we study Enneper type representations for minimal surfaces in the Euclidean space R3 and for maximal surfaces in the Lorentz-Minkowski space L3, using complex analysis, and we study an Enneper type representation for minimal timelike surfaces in L3, using paracomplex analysis. Thus we introduce some results of complex and paracomplex analysis and we use them to prove theorems of Weierstrass representation in R3 e L3. Some examples of minimal surfaces inR3 and L3, will be constructed via Enneper representation formula, which is equivalent to theWeierstrass representation formula for the same surfaces.
 
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Publishing Date
2021-07-06
 
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