Enneper representation of minimal surfaces in the Euclidean and Lorentz-Minkowski ...
Geometry of manifolds in the euclidian space and in the Minkowski space
An introduction to differential geometry of curves and surfaces in Minkowski space
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Enneper representation of minimal surfaces in the Euclidean and Lorentz-Minkowski spaces
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| Author(s): |
Bruna Vieira da Silva Flores
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2021-04-05 |
| Examining board members: |
Rosa Maria dos Santos Barreiro Chaves;
Fernanda Ester Camillo Camargo;
Eliane da Silva dos Santos
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| Advisor: | Rosa Maria dos Santos Barreiro Chaves |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 18/25992-0 - Enneper representation of minimal surfaces in the Euclidean and Lorentz-Minkowski spaces |
| Grantee: | Bruna Vieira da Silva Flores |
| Support Opportunities: | Scholarships in Brazil - Master |