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| Author(s): |
Carlos Henrique Silva Alcantara
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2019-07-19 |
| Examining board members: |
Claudio Gorodski;
Igor Leite Freire;
Rafael de Freitas Leão
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| Advisor: | Claudio Gorodski |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 17/08206-8 - Moving frames and exterior differential systems |
| Grantee: | Carlos Henrique Silva Alcantara |
| Support Opportunities: | Scholarships in Brazil - Master |