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 thesis
Geometry, Riemannian
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

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