Differential Geometry II Spring 2022

Joaquim Serra
Tommaso Goldhirsch
Time and Location:
Monday, 14:15 - 16:00 in HG G 5
Thursday, 10:15 - 11:55 in CAB G 11


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.


Differential Geometry I (or basics of differentiable manifolds).

Lecture and Video Recordings

Lectures will take place in-person and will be live streamed. According to the current ETH Guidelines, wearing a maks is mandatory in places indoors.

The lecture will be streamed live on the ETH Video Portal.
Recordings will be available here on the morning of the following day.

Time Room Livestream
Monday 14:15-16:00 HG G 5 Livestream HG G 5
Thursday 10:15-11:55 CAB G 11 Livestream CAB G 11

See the official documentation for more tecnical informations.


The new exercise sheet will be uploaded on this page on Monday. 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 Monday at 12:15 to upload your solutions.
The first exercise sheet will be uploaded the second week of the semester.

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 Upload Sheet 1 Solution 1
Exercise Sheet 2 March 14 Upload Sheet 2 Solution 2
Exercise Sheet 3 March 21 Upload Sheet 3 Solution 3
Exercise Sheet 4 March 28 Upload Sheet 4 Solution 4
Exercise Sheet 5 April 4 Upload Sheet 5 Solution 5
Exercise Sheet 6 April 11 Upload Sheet 6 Solution 6
Exercise Sheet 7 April 25 Upload Sheet 7 Solution 7
Exercise Sheet 8 May 9 Upload Sheet 8 Solution 8
Exercise Sheet 9 May 16 Upload Sheet 9 Solution 9
Exercise Sheet 10 May 23 Upload Sheet 10 Solution 10
Exercise Sheet 11 May 30 Upload Sheet 11 Solution 11

Exercise classes

The exercise classes will start the second week of the semester. You can enrol in one exercise class on MyStudies

Fr 09-10HG E 1.1Giovanni Ambrosionien
Fr 10-11HG E 1.1Federico Franceschinien