Differential Geometry I Autumn 2019
- Lecturer:
- Urs Lang
- Coordinator:
- Tommaso Goldhirsch
- Time and Location:
- Monday, 13:15 - 15:00 in ML H 44 and Wednesday, 13:15 - 15:00 in HG G 5
Content
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.
Exam
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.
Exercises
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 classes
| time | room | assistant | language |
|---|
| Th 14-15 | HG E 21 | Xenia Lorena Flamm | en |
| Th 15-16 | HG F 26.5 | Tommaso Goldhirsch | en |
| Fr 13-14 | HG F 3 | Giuliano Basso | en |
Literature
Differential Geometry in Rˆn:
-
Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces
-
Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten
-
Christian Bär: Elementare Differentialgeometrie
Differential Topology:
-
Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds
-
Victor Guillemin & Alan Pollack: Differential Topology
-
Morris W. Hirsch: Differential Topology
Partial lecture notes from the course taught in Fall 2016 (in German) are available
from
Prof. Lang's website.