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