Math 42, Winter 2006,
Differential Geometry I
Covered topics
- 1. Curves
- Length and parametrizations
- Curvature, torsion and the Frenet formulae
- Isoperimetric Inequality
- 2. Surfaces and Curvature
- Surfaces: parametrizations and graphs
- The tangent space and vector fields
- Immersed and Embedded surfaces
- The normal vector and Guass map
- Curvatures
- Parallel transport
- 3. Geodesics and Isometries
- Surfaces as metric spaces
- Geodesics
- Geodesic equations: connections and curvature
- Isometries
As time permits, some of the following topics
- Constant Mean Curvature Surfaces
- Topology and geometry: Euler characteristic and the Gauss-Bonnet Theorem
- Abstract Surfaces
- Higher dimensions