An introduction to differential geometry of curves and surfaces in Minkowski space

• Grant number: 20/05978-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2020
• Effective date (End): February 28, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Carlos Ferreira Costa
• Grantee: Tiago Suzuki Tokuda
• 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
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

The goal of this work is to approach the study of curves and surfaces in the Minkowski space (or also called Lorentz-Minkowski space), having as a starting point the classic elements of Differential Geometry of curves and surfaces in the Euclidean space. We investigate what are the points which are affected or not bymetric change. Also, we want to know the differences and similarities between some concepts and results in these two contexts (euclidian and Minkowski context). This subject is a research topic in Differential Geometry as well as being of great interest in Singularity theory, with many applications in different contexts, such as in Physics. It is a wide topic, but it will be adapted for research at the level of scientific initiation. We think that it is a good opportunity for the student as an introduction to research in Mathematics at a more advanced level.