The Gauss-Bonnet theorem, the Euler-Poincare characteristic and applications

• Grant number: 13/07871-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2013
• End date: January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Carlos Ferreira Costa
• Grantee: Thales Augusto Leite de Souza
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

The main goal of this plan is to study aspects from the geometry and the topology of surfaces based in the beautiful Gauss-Bonnet theorem. In fact, the Gauss Bonnet theorem presents a good relationship between the geometry of the surface (the Gaussian curvature) and the topological aspects of the surface (Euler-Poincare characteristic). Some physical applications will be studied based on a scientific paper. (AU)