21-759 Differential Geometry

12 units, Carnegie Mellon University

Manifolds in Euclidean spaces, curves and surfaces, principal curvatures, geodesics. Surfaces with constant mean curvature, minimal surfaces. Abstract differentiable manifolds, tangent spaces, vector bundles, affine connections, parallelisms, covariant gradients, Cartan torsion, Riemann curvature. Riemannian geometry, Lie groups. Familiarity with analysis in finite dimensional spaces will be assumed. Three 50 minute lectures

Prerequisites: (21-356 (min B) or 21-236 (min B) or 21-456 (min B)) and (21-373 (min B) or 21-237 (min B))

Offered: Spring 2027

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