Differential Geometry

12 units · Graduate

Intermittent: 12 units 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: ( 21-456 Min. grade B or 21-356 Min. grade B or 21-236 Min. grade B) and ( 21-373 Min. grade B or 21-237 Min. grade B)