García López, Ricardo, 1962-Novell Masot, Sergi2021-06-022021-06-022020-06-16https://hdl.handle.net/2445/177883Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López[en] In this work, we study Riemannian and pseudo-Riemannian manifolds and their main properties. From them, we examine the special and general theories of relativity, and see how they arise from modelling space-time as special kinds of pseudoRiemannian manifolds, the Lorentzian manifolds. Within this theory, we are able to give a rigorous formulation of the fundamental properties of cosmology and the Schwarzschild space-time. We also wish to relate the behaviour of geodesics in a manifold with the intrinsic structure of the manifold. This results in the formulation of the Hopf-Rinow theorem in the case of Riemannian manifolds, and the Hawking singularity theorem, in Lorentzian manifolds.59 p.application/pdfengcc-by-nc-nd (c) Sergi Novell Masot, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Varietats diferenciablesTreballs de fi de grauGeometria diferencialRelativitat general (Física)Differentiable manifoldsBachelor's thesesDifferential geometryGeneral relativity (Physics)info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess