Mathematics 230A

Differential Geometry (113369)

Dan Freed

2026 Fall (4 Credits)

Schedule: MW 1030 AM - 1145 AM

Instructor Permissions: None

Enrollment Cap: n/a

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.

Recommended Prep:

Knowledge of the material in Mathematics 132 and 136.

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