Differential geometry and applications

• Grant number: 17/21283-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2017
• End date: October 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Irene Ignazia Onnis
• Grantee: Vinicius Meirelles Partel
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project of scientific initiation proposes to introduce the student to the Differential Geometry through the study of some interesting topics of the local theory of curves and surfaces in the three-dimensional Euclidean space, which are important tools for modeling problems in different areas as Biology, Statistics, Physics and Engineering.In particular, as applications of the topics studied to Civil Engineering, we will see the use of the catenary arc by Robert Maillart in the construction of the bridges and also, how the engineer Otto Frei could bring to reality the forms of the soap films (which are physical models of minimal surfaces) to realize light, stable, luminous and low cost covering. (AU)