Differential Geometry

Harvard FAS

The overarching theme is the Felix Klein dictum that places symmetry groups at the center of geometry. Topics include: affine geometry and symmetry types, smooth manifolds and Lie groups, Frobenius theorem; classical curves and surfaces; fiber bundles, principal bundles, connections, geodesics, curvature, torsion; Riemannian manifolds, Levi-Civita connection, Riemann curvature tensor; Gauss-Bonnet-Chern theorem; more Riemannian geometry.