Differential Geometry I Autumn 2022

Joaquim Serra
Tommaso Goldhirsch
Time and Location:
Monday, 14:15 - 16:00 in HG D 1.2
Wednesday, 14:15 - 16:00 in HG D 1.2


Introduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in \(\mathbb{R}^n\), geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.

The course will follows the Differential Geometry I course taught by Prof. Urs Lang in 2019 (see literature below).


The handwritten slides from the lecture are available here: part 1, part 2 and part 3.

Lecture and Video Recordings

Lectures will take place in-person and will be live streamed.

The lecture will be streamed live on the ETH Video Portal.
Recordings will be available here, usually the morning after the lecture.

Time Room Livestream
Monday 14:15 - 16:00 HG D 1.2 Livestream HG D 1.2
Wednesday 14:15 - 16:00 HG D 1.2 Livestream HG D 1.2

See the official documentation for more tecnical informations.

Recordings of last year's Differential Geometry I (HS 21) are also available on the ETH video platform.


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.

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 October 3, 12:15 Upload Sheet 1 Solution 1
Exercise Sheet 2 October 10, 12:15 Upload Sheet 2 Solution 2
Exercise Sheet 3 October 17, 12:15 Upload Sheet 3 Solution 3
Exercise Sheet 4 October 24, 12:15 Upload Sheet 4 Solution 4
Exercise Sheet 5 November 7, 12:15 (NEW!) Upload Sheet 5 Solution 5
Exercise Sheet 6 November 14, 12:15 Upload Sheet 6 Solution 6
Exercise Sheet 7 November 28, 12:15 (NEW!) Upload Sheet 7 Solution 7
Exercise Sheet 8 December 5, 12:15 Upload Sheet 8 Solution 8
Exercise Sheet 9 December 12, 12:15 Upload Sheet 9 Solution 9
Exercise Sheet 10 December 17, 12:15 Upload Sheet 10 Solution 10
Exercise Sheet 11 December 29, 12:15 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

Thursday 13-14HG E 22Alessandro Audritoen
Thursday 16-17IFW C 33Alessio Pellegrinien
Friday 13-14HG F 3Patricia Dietzschen


The exam took place Friday 27th of February. Here you can find the exam and the solutions.

Here you can find the exams of last year's course in Differential Geometry. SPOILER ALERT! Don't open the solutions unless you really want to see them.

The exams: HS21 Exam (Winter) and HS21 Exam (Summer).

The solutions: HS21 Solutions (Winter) and HS21 Solutions (Summer).


Partial lecture notes from the course taught in Fall 2019 are available from Prof. Lang's website.