Introduction to Differential Geometry: Manifolds, Geometry Riemannian and Fibrates

• Grant number: 23/10690-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2023
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Fernando David Marmolejo Schmidtt
• Grantee: Arthur Costa Rodrigues
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Differential Geometry originated from the manipulation between calculus and geometry, having as oneof its main objectives the study of curves and surfaces. Initially used for the study ofcartography, however, over the centuries it became necessary for the study and development of physical theories. Today, it has its presence in the most diverse areas of physics,such as Mechanics, Classical Thermodynamics, Electromagnetism, and especially the General Theory of Relativity, which is inconceivable without this mathematical branch. Stick to what was presentedSo far, such research aims to introduce the student to this mathematical and physical field,in the case of important substances, such as: variety - real and complex -, ana Riemannian Geometry, and bundles - of configurations and connections. In this bias, the aim is to prove to the student the discernment andthe necessary basis for a future in-depth study in the area of Theoretical Physics, because even havinga great importance, the teaching of this mathematics is reduced during the graduation in physics.