This is a continuation course of Differential Geometry I. Topics covered include: Introduction to Riemannian geometry: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, and isoperimetric inequalities.
For the first chapter on differential manifolds (recap), vector bundles, vector fields, and flows we will use chapters 8 and 10 from the lecture notes on Differential Geometry I by Prof. Lang. You can find it here. For most of the rest of the course, we will use Prof. Lang's notes which were sent by email to all registered students.
Prerequisites: Differential Geometry I (or basics of differentiable manifolds)
Here are the handwritten
slides from the lecture:
Notes
Lectures will take place in-person and will be recorded.
Recordings will be available here, usually the morning after the lecture.
The new exercise sheet will be uploaded on this page on Tuesday. You are supposed to have a look at it before the exercise class, so that you can ask questions if you need to. You have time until the following Tuesday at 12:15 to upload your solutions.
Please, upload your solution via the SAM upload tool.
In order to access the website you will need a NETHZ-account and you will have to be connected to the ETH-network. From outside the ETH network you can connect to the ETH network via VPN. Here are instructions on how to do that.
Make sure that your solution is one PDF file and that its file name is formatted in the following way:
solution_<number of exercise sheet>_<your last name>_<your first name>.pdf
Example:
solution_2_Surname_Name.pdf.
| Exercise Sheet | Due By | Upload Link | Solutions |
|---|---|---|---|
| Exercise Sheet 1 | March 7, 12:15 | Upload Sheet 1 | Solution 1 |
| Exercise Sheet 2 | March 14, 12:15 | Upload Sheet 2 | Solution 2 |
| Exercise Sheet 3 | March 21, 12:15 | Upload Sheet 3 | Solution 3 |
| Exercise Sheet 4 | March 28, 12:15 | Upload Sheet 4 | Solution 4 |
| Exercise Sheet 5 | April 4, 12:15 | Upload Sheet 5 | Solution 5 |
| Exercise Sheet 6 | April 18, 12:15 | Upload Sheet 6 | Solution 6 |
| Exercise Sheet 7 | April 25, 12:15 | Upload Sheet 7 | Solution 7 |
| Exercise Sheet 8 | Mai 2, 12:15 | Upload Sheet 8 | Solution 8 |
| Exercise Sheet 9 | Mai 9, 12:15 | Upload Sheet 9 | Solution 9 |
| Exercise Sheet 10 | Mai 16, 12:15 | Upload Sheet 10 | Solution 10 |
| Exercise Sheet 11 | Mai 23, 12:15 | Upload Sheet 11 | Solution 11 |
The exercise classes will start the second week of the semester. You can enrol in one exercise class on MyStudies
NEW: Starting from 28.4. there will only be ONE exercise class, namley at 9:15 - 10:00. After class we'll take the time to answer questions (in HG E 1.1).
| time | room | assistant | language |
|---|---|---|---|
| Fr 09-10 | HG E 1.1 | Giacomo Colombo and Patricia Dietzsch | English |
| Fr 10-11 | HG E 1.1 | Time for Q&A | English |