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memoria.pdf (657.88 KB)

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Bachelor thesis

Publication date

2016-06-27

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cc-by-nc-nd (c) Alejandro Fernández Piqué, 2016
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/108742

Twistor theory and gravitational instantons

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Abstract

The aim of this work is to understand and introduce a self-contained account of the construction of certain kind of gravitational instantons made by Hitchin in his work “Polygons and Gravitons”. Gravitational instantons are solutions of the Einstein equations which have a complete, non-singular and positive definite metric. Hitchin use twistor theory to construct these solutions. We present beforehand some concepts of self-duality, differential operators and connections to understand twistor theory. Afterwards, the construction of the aforementioned instantons is explained in full detail.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Ignasi Mundet i Riera

Subject

Geometria algebraica, Treballs de fi de grau, Geometria de Riemann, Equacions diferencials, Física matemàtica

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Algebraic geometry, Bachelor's theses, Riemannian geometry, Differential equations, Mathematical physics

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

FERNÁNDEZ PIQUÉ, Alejandro. Twistor theory and gravitational instantons. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/108742

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