Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/140379
Title: | The isometry group of semi-Riemannian manifolds |
Author: | Llorens Giralt, Quim |
Director/Tutor: | Mundet i Riera, Ignasi |
Keywords: | Grups de Lie Treballs de fi de grau Geometria de Riemann Geometria diferencial global Varietats diferenciables Lie groups Bachelor's theses Riemannian geometry Global differential geometry Differentiable manifolds |
Issue Date: | 18-Jan-2019 |
Abstract: | [en] This work presents two important subjects of modern mathematics, Lie Groups and semi-Riemannian Geometry, and shows a beautiful theorem that arises as a combination of both matters: the isometry group of a semi-Riemannian manifold is a Lie group. The structure of the proof presented is as follows. First, we introduce a theorem by Palais [1], which gives a sufficient condition for a group G of diffeomorphisms acting on a smooth manifold M to be a Lie group: that the set of all vector fields on M which generate global 1-parameters subgroups of G generates a finite-dimensional Lie algebra. Then we show that this result can be applied to the isometry group of semi-Riemannian manifolds, by proving that the set of all complete Killing vector fields generates a finite-dimensional Lie algebra. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Ignasi Mundet i Riera |
URI: | http://hdl.handle.net/2445/140379 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Llorens_Giralt_Quim_TFG.pdf | Memòria | 434.19 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License