Gauss-Bonnet theorem and applications
Date
2014Authors
Rodríguez Ramírez, Juan CamiloDirectors
Vargas Domínguez, AndrésPublisher
Pontificia Universidad Javeriana
Faculty
Facultad de Ciencias
Program
Matemáticas
Obtained title
Matemático (a)
Type
Tesis/Trabajo de grado - Monografía - Pregrado
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Resumen
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.
Abstract
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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