Category
Manifolds
Related lectures (132)
Conformal Maps and Hyperbolic Geometry
Explores conformal maps, hyperbolic geometry, and isometric properties of disks.
Local Homeomorphisms and Coverings
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.
Closed Surfaces and Integrals
Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
Building surfaces from equilateral triangles
Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.
Geodesics on Surfaces
Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.
Gaussian Curvature and Geodesics
Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Geometric Surfaces: Paraboloids and Hyperboloids in Architecture
Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.