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Master's Dissertation
DOI
Document
Author
Full name
Carlos Henrique Silva Alcantara
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Gorodski, Claudio (President)
Freire, Igor Leite
Leão, Rafael de Freitas
Title in Portuguese
O método do referencial móvel e sistemas diferenciais exteriores
Keywords in Portuguese
Fórmula de Gauss-Bonnet
Referenciais móveis
Teoria de Cartan-Kähler
Abstract in Portuguese
Nesse trabalho, estudamos o método do referencial móvel e sistemas diferenciais exteriores. Estabelecemos resultados de Geometria Riemanniana via referenciais móveis e com essa linguagem introduzimos o Teorema de Gauss-Bonnet-Chern e apresentamos uma adaptação da demonstração original de S.-S. Chern presente no artigo A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Ao abordar aspectos da teoria de Cartan-Kähler, codificamos as ideias oriundas dos referenciais móveis em sistemas diferenciais exteriores e mostramos algumas aplicações à Geometria Riemanniana.
Title in English
Moving frames and exterior differential systtems.
Keywords in English
Cartan-Kähler theory
Gauss-Bonnet formula
Moving frames
Abstract in English
In this work, we study the method of moving frame and exterior differential systems. We set up results of Riemannian Geometry via moving frames and with this language we introduce the Gauss-Bonnet-Chern Theorem and present an adaptation of the original proof of S.-S. Chern in the article A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. In discussing aspects of Cartan-Kählers theory, we encode the ideas from moving frames into exterior differential systems and use this tool in Riemannian Geometry.
 
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diss_corrigida.pdf (769.88 Kbytes)
Publishing Date
2019-10-02
 
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