Study of surfaces with mean curvature one in the hyperbolic space

• Grant number: 17/20667-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): December 01, 2017
• Effective date (End): November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Rosa Maria dos Santos Barreiro Chaves
• Grantee: Bruna Vieira da Silva Flores
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we study the minimal surfaces in R^3 and the surfaces with mean curvature one in the hyperbolic space H^3. The student already studied the theory of curves and surfaces in the Euclidean and in the hyperbolic space in a previous project and got interested in continuing her study in the hyperbolic space. Then, in this second proposal we are interested in studying minimal surfaces, via Weierstrass representation, to be prepared to study also the Weierstrass representation for the surfaces with mean curvature one in the hyperbolic space. It is possible to make a comparison between both Weierstrass representation. We will use the software Mathematica as an extra tool in our studies, in order to obtain a better visualization of the examples and a better comprehension of the theory. The University of São Paulo has a site license of that software, that let interested teachers and students to use it. In this way, the student will have also access to that further tool, during the seminars for the development of her project. (AU)