Tensors, manifolds and differential geometry: applications in mechanics and relativity

• Grant number: 14/15527-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2014
• End date: September 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Maurício Richartz
• Grantee: Thiago Assumpção
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated research grant: 13/09357-9 - Physics and geometry of spacetime, AP.TEM

Abstract

A detailed and mathematically rigorous analysis of fundamental concepts of Mathematical Physics is proposed, including applications in Relativity and Mechanics. The research proposal initially includes the study of multilinear algebra, tensors and basic topology. Subsequently, Differential Geometry will be the main focus - differentiable manifolds, tangent spaces, curvatures, differential forms, integration and Stokes theorem will be studied. In the project's last stage, the student will conduct an introductory study of General Relativity and Hamiltonian formalism of Classical Mechanics, applying the previously developed concepts. At the end of the project, the student is expected to have a solid background on Differential Geometry which will allow him, in the future, to continue his studies in Physics or Mathematics.