| 1 |
19.02 |
Introduction, Riemannian metrics
|
| 22.02 |
vector and tensor bundles (1.3) |
| 2 |
26.02. |
length and volumes (2.1, 2.2), connections on vector bundles (3: intro) |
| 29.02. |
Levi-Civita connection, vector fields along maps (3.1) |
| 3 |
04.03 |
parallel transport (3.2), first variation of length (3.3), geodesics (beginning of 4) |
| 07.03. |
Gauss lemma, local length minimization of geodesics (4.1) |
| 4 |
11.03 |
Hopf-Rinow theorem (4.2) |
| 14.03. |
Riemann curvature tensor(5.1) |
| 5 |
18.03 |
Sectional curvature (5.2), Contractions (5.3) |
| 21.03. |
Contractions (5.3, continued), operations on tensors II (5.4) |
| 6 |
25.03 |
Second Bianchi identity and applications (5.4) |
| 28.03. |
Curvature of submanifolds (5.5), second variation of length (6.1) |
| 7 |
8.04 |
Jacobi fields (6.1) |
| 11.04 |
Conjugate points (6.1), second variation of length (6.2) |
| 8 |
18.04 |
Synge's Theorem (6.3), space forms (beginning of 7) |
| 9 |
22.04 |
Covering maps (7.1) |
| 25.04 |
End of covering maps (7.1), Proof of Killing-Hopf Theorem (7.2,7.3) |
| 10 |
29.04 |
Cartan-Hadamard manifolds (8) |
| 02.05 |
Cartan-Hadamard manifolds (8), continued |
| 11 |
06.05 |
Differential forms (9.1 and 9.2) |
| 12 |
13.05 |
Exterior derivative and orientation (9.3 and 9.4) |
| 16.05 |
Stokes' theorem and orientation (9.4 and 9.5) |
| 13 |
20.05 |
Cohomology, Meyer-Vietoris sequence (9.6) |
| 23.05 |
Convex neighbourhoods (9.7) |
| 14 |
27.05 |
Poincaré duality (9.8) |
| 30.05 |
review |