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http://hdl.handle.net/2445/140379
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DC Field | Value | Language |
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dc.contributor.advisor | Mundet i Riera, Ignasi | - |
dc.contributor.author | Llorens Giralt, Quim | - |
dc.date.accessioned | 2019-09-18T08:34:10Z | - |
dc.date.available | 2019-09-18T08:34:10Z | - |
dc.date.issued | 2019-01-18 | - |
dc.identifier.uri | http://hdl.handle.net/2445/140379 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Ignasi Mundet i Riera | ca |
dc.description.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. | ca |
dc.format.extent | 65 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Quim Llorens Giralt, 2019 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Grups de Lie | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Geometria de Riemann | ca |
dc.subject.classification | Geometria diferencial global | ca |
dc.subject.classification | Varietats diferenciables | ca |
dc.subject.other | Lie groups | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Riemannian geometry | en |
dc.subject.other | Global differential geometry | en |
dc.subject.other | Differentiable manifolds | en |
dc.title | The isometry group of semi-Riemannian manifolds | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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Llorens_Giralt_Quim_TFG.pdf | Memòria | 434.19 kB | Adobe PDF | View/Open |
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