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tfg_atencia_sanmiguel_josep.pdf (1.26 MB)

Document type

Bachelor thesis

Publication date

2023-06-13

Publication license

cc-by-nc-nd (c) Josep Atencia San Miguel, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/202524

El teorema de Killing-Hopf

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Abstract

[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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Ricardo García López

Subject

Geometria diferencial, Treballs de fi de grau, Geometria de Riemann, Varietats de Riemann

Subject (English)

Differential geometry, Bachelor's theses, Riemannian geometry, Riemannian manifolds

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

ATENCIA SAN MIGUEL, Josep. El teorema de Killing-Hopf. [consulted: 10 of June of 2026]. Available at: https://hdl.handle.net/2445/202524

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