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Enneper representation of minimal surfaces in the Euclidean and Lorentz-Minkowski spaces

Grant number: 18/25992-0
Support type:Scholarships in Brazil - Master
Effective date (Start): April 01, 2019
Effective date (End): March 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Rosa Maria dos Santos Barreiro Chaves
Grantee:Bruna Vieira da Silva
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The main purpose of this project is to study Enneper type representations for minimal surfaces in the Euclidean space R3 and for minimal spacelike and timelike surfaces in the Lorentz-Minkowski space L3, using complex and paracomplex analysis, respectively. Some examples of minimal surfaces in R3 e L3 will be constructed via Enneper representation formula, which is equivalent to the Weiestrass representation formula for the same surfaces. Two papers will be used as a basis for the development of the project, one of them related to the Euclidean Enneper representation and the other to the Lorentzian Enneper representations. The method via Enneper representation has the advantage of allowing greater simplicity in computational calculus and of providing the construction of a conformal minimal immersion from a harmonic function.