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Master's Dissertation
DOI
Document
Author
Full name
Lucas de Faccio Nunes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Valério, Barbara Corominas (President)
Sousa Junior, Luiz Amancio Machado de
Vilhena, José Antônio Moraes
Title in Portuguese
Um estudo sobre incompletude de geodésicas semi-Riemannianas
Keywords in Portuguese
Completude de geodésicas
Geodésicas
Métricas de Lorentz
Abstract in Portuguese
Nesse trabalho apresentaremos alguns exemplos clássicos que evidenciam as diferenças entre a geometria Riemanniana e a semi-Riemanniana (Lorentziana) quanto à completude de geodésicas. Para isso, revisitaremos conceitos básicos de Geometria, seguido de uma introdução aos espaços vetoriais de Lorentz e um estudo inicial sobre o grupo de Lorentz. Nos capítulos finais discutiremos sobre completude de geodésicas e como se distanciam do caso Riemanniano.
Title in English
A study on uncompleteness of semi-Riemannian geodesics
Keywords in English
Completeness of geodesics
Geodesic
Lorentz metrics
Abstract in English
In this work we intend to present some classical examples that display the differences between Riemannian and semi-Riemannian (Lorentzian) geometry in relation to the completeness of geodesics. For this, we will revisit basic Geometry concepts followed by an introduction to the vector spaces of Lorentz and a simple study on the Lorentz group. In the final chapters we will discuss about the completeness of geodesics and how it distances itself from the Riemannian case.
 
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Publishing Date
2019-09-09
 
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