Differential Geometry I Autumn 2019

Urs Lang
Tommaso Goldhirsch
Time and Location:
Monday, 13:15 - 15:00 in ML H 44 and Wednesday, 13:15 - 15:00 in HG G 5


Introduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in 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, de Rham cohomology.


The exam took place Monday, February 3rd 2020. Here you can find the exam and the solutions.
The repetition exam took place Saturday, August 15th 2020. Here you can find the exam and the solutions.


The new exercise sheet will be posted here 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 until the following Monday to hand it in, before 12:15 in the box of you theaching assistant in room HG J68.

exercise sheet due by solutions
Exercise sheet 1 30.09.19 Solutions 1
Exercise sheet 2 07.10.19 Solutions 2
Exercise sheet 3 14.10.19 Solutions 3
Exercise sheet 4 21.10.19 Solutions 4
Exercise sheet 5 28.10.19 Solutions 5
Exercise sheet 6 04.11.19 Solutions 6
Exercise sheet 7 11.11.19 Solutions 7
Exercise sheet 8 18.11.19 Solutions 8
Exercise sheet 9 25.11.19 Solutions 9
Exercise sheet 10 2.02.19 Solutions 10
Exercise sheet 11 9.02.19 Solutions 11
Exercise sheet 12 16.02.19 Solutions 12
Exercise sheet 13 - Solutions 13

Exercise classes

Th 14-15HG E 21Xenia Lorena Flammen
Th 15-16HG F 26.5Tommaso Goldhirschen
Fr 13-14HG F 3Giuliano Bassoen


Differential Geometry in Rˆn: Differential Topology: Partial lecture notes from the course taught in Fall 2016 (in German) are available from Prof. Lang's website.