Mundet i Riera, IgnasiFernández Piqué, Alejandro2017-03-222017-03-222016-06-27https://hdl.handle.net/2445/108742Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Ignasi Mundet i RieraThe 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.51 p.application/pdfengcc-by-nc-nd (c) Alejandro Fernández Piqué, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/esGeometria algebraicaTreballs de fi de grauGeometria de RiemannEquacions diferencialsFísica matemàticaAlgebraic geometryBachelor's thesesRiemannian geometryDifferential equationsMathematical physicsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess