Mundet i Riera, IgnasiMaravall López, Javier2022-05-102022-05-102021-06-20https://hdl.handle.net/2445/185428Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ignasi Mundet i Riera[en] The Gauss-Bonnet theorem is one of the earliest classical results in differential geometry. It provides a link between the topology and the geometry of a smooth surface (that is, a smooth 2-manifold). A well-known, highly non-trivial generalisation of this to arbitrary (finite) dimension exists, which was first proven intrinsically (in other words, without recourse to the existence of an embedding of the manifold into an Euclidean space) by Shiing-Shen Chern in 1944. The aim of this work is to provide a full proof of a slightly more general result, which is valid for arbitrary vector bundles over a differential manifold, that gives as a direct corollary the Gauss-Bonnet-Chern theorem when considering the tangent bundle.80 p.application/pdfengcc-by-nc-nd (c) Javier Maravall López, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Formes diferencialsTreballs de fi de grauGeometria diferencialVarietats diferenciablesDifferential formsBachelor's thesesDifferential geometryDifferentiable manifoldsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess