Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.
Explores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.
Explores surfaces with constant null curvature and their development, as well as the construction of networks of curves in hyperbolic paraboloids.
Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.
