Course overview
The geometry of Euclid, flat space geometry, was believed for a long time to be the only geometry possible. In the 19th century examples were produced of curved space geometries, by various authors. Of these, the most far-reaching and general was developed by B. Riemann. This course is a modern introduction to Riemanns geometry, starting from the notion of smooth manifold, Riemannian metric, connections, geodesics, and curvature. This proved the ideal setting for Einsteins study of relativity, for instance.
Course learning outcomes
- Demonstrate an understanding of the intrinsic geometry of manifolds
- Apply the general theory to specific examples
- Produce sophisticated arguments and proofs, at the appropriate level
- Communicate results clearly