García López, Ricardo, 1962-Atencia San Miguel, Josep2023-10-052023-10-052023-06-13https://hdl.handle.net/2445/202524Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Ricardo García López[en] Driven by the study of the universe’s geometry, the Killing-Hopf theorem classifies the riemannian manifolds with constant sectional curvature, identifying them as the quotient of an euclidean space, a spherical space or a hyperbolic space. Starting from a theoretical foundation in differential geometry, in this essay we develop a proof of the theorem, focused on the application of geodesics curves and their metric properties in riemannian manifolds.52 p.application/pdfspacc-by-nc-nd (c) Josep Atencia San Miguel, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Geometria diferencialTreballs de fi de grauGeometria de RiemannVarietats de RiemannDifferential geometryBachelor's thesesRiemannian geometryRiemannian manifoldsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess