Gauss-Bonnet theorem and applications
Data
2014Direttore
Vargas Domínguez, AndrésPublishers
Pontificia Universidad Javeriana
facoltà
Facultad de Ciencias
programma
Matemáticas
Titolo ottenuto
Matemático (a)
Tipo
Tesis/Trabajo de grado - Monografía - Pregrado
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Sommario
Este trabajo tiene como fin estudiar el caso general del teorema de Gauss- Bonnet para superficies compactas orientadas sin frontera conocido como el teorema de Gauss-Bonnet-Chern el cual provee una relación fundamental entre la geometría del espacio y su topología. Para ello se estudiaron temas tales como variedades Riemannianas, formas diferenciales en variedades, característica de Euler, entre otros.
Astratto
This thesis work is devoted to study the general case of the Gauss-Bonnet Theorem for compact oriented surfaces without boundary known as the Gauss-Bonnet-Chern Theorem which provides a fundamental relationship between the geometry of the space and its topology. For that some topics frequently used in this area were studied, we can mention Riemannian manifolds, differential forms on manifold and with values in a Lie algebra, Euler characteristic, among others.
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