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Llorens_Giralt_Quim_TFG.pdf (434.19 KB)

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Bachelor thesis

Publication date

2019-01-18

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cc-by-nc-nd (c) Quim Llorens Giralt, 2019
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/140379

The isometry group of semi-Riemannian manifolds

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Ignasi Mundet i Riera

Subject

Grups de Lie, Treballs de fi de grau, Geometria de Riemann, Geometria diferencial global, Varietats diferenciables

Subject (English)

Lie groups, Bachelor's theses, Riemannian geometry, Global differential geometry, Differentiable manifolds

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

LLORENS GIRALT, Quim. The isometry group of semi-Riemannian manifolds. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/140379

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