Ferramentas elementares para geometrias classicas e hiperbolica complexa

TL;DRAbstract

This thesis consists of four parts. The first part consists of a construction interpreting all classic geometries in the same way. With this construction, we express and characterize various aspects of these geometries, such as geodesics, distances, parallel displacement, curvature tensors, and sectional curvatures, in a simple coordinate-free way. We believe that this approach can unify and simplify the study of classic geometries escaping the use of several "models" for the same geometry (as Poincar's, Siegel's, and Klein's models of hyperbolic geometry) as well as avoiding descriptions of metrics in specific coordinates.

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