| Tuesday | Thursday |
|---|---|
|
|
Sept 10 Overview of the plan for the class - preview of things to come. notes |
|
Sept 15 Prerequisites - k-submanifolds of R^n. notes |
Sept 17 Tangent space - curves. notes |
|
Sept 22 Frenet curves - curvature - torsion notes |
Sept 24 Curves constrained to surfaces notes |
|
Sept 29 Frenet curves in R^n notes |
Oct 1 Global theory of curves - winding number - rotation index notes |
|
Oct 6 Surfaces - metric - first fundamental form - vector fields notes |
Oct 8 Gauss map - shape operator notes |
|
Oct 13 Tuesday = Monday = no class |
Oct 15 Priciple curvatures - Gaussian and Mean curvature notes |
|
Oct 20 Examples of curvature computations notes |
Oct 22 Hypersurfaces (sorry - no legible notes) (Take-home midterm to be passed out) |
|
Oct 27 Covariant derivative notes Take-home midterm due |
Oct 29 Christoffel symbols notes |
|
Nov 3 Geodesics and parallel transport notes |
Nov 5 Theorem Egregium notes |
|
Nov 10 Theorem Egregium, cont'd. |
Nov 12 Calculating curvature - more tensors - does curvature determine surface? notes |
|
Nov 17 Calculating curvature - more tensors - does curvature determine surface? cont'd. |
Nov 19 Differential forms. notes |
|
Nov 24 Differential forms, cont'd. Euler Characteristic. notes on Euler characteristic |
Nov 26 THANKSGIVING HOLIDAY |
|
Dec 1 Connection forms - curvature forms. notes |
Dec 3 Gauss-Bonnet Theorem. notes |
|
Dec 8 General Riemannian Manifolds notes |
Dec 10 Sectional curvature - uniformization of surfaces notes |