Differential geometry of curves and surfaces

• Grant number: 12/03075-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): April 01, 2012
• Effective date (End): December 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Irene Ignazia Onnis
• Grantee: Iberê Oliveira Kuntz de Souza
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This undergraduate research project is aimed at a good physics student who is strongly interested in studying the local theory of surfaces and in particular, in developing this theory also using the method of E. Cartan, called the method of the moving frames. Therefore, I elaborated the project with the purpose of providing to the student the bases to understand this last topic. The theme of the project permits that the student uses studied concepts and methods in the disciplines of analytical geometry, calculus (differential and integral) and linear algebra. As is a first contact of the student with the Differential Geometry, the involved concepts in the topics are illustrating through various examples. We will also use the software MATHEMATICA to perform some graphic illustrations that will help the student to understand the topics of the project. I emphasize that the study of the theory will be always accompanied by the resolution of exercises, and the most important exercises will be included in the final report. In this way the student will experience as to design a didactic material. (AU)