Abstract
We expect the student to dedicate himself to the study of hyperbolic geometry in its various facets, from metric spaces of non-positive curvature (à la Alexandrov) to Hadamard manifolds and riemannian manifolds of negative curvature (pinched or not). To avoid a dangerous and unmotivated 'study by itself,' the project is surrounded by a known and concrete problem in real hyperbolic geometr…