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 GaussBonnet. 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 1415  HG E 21  Xenia Lorena Flamm  en 
Th 1516  HG F 26.5  Tommaso Goldhirsch  en 
Fr 1314  HG F 3  Giuliano Basso  en 
Literature
Differential Geometry in Rˆn:

Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces

Wolfgang Kühnel: Differentialgeometrie. KurvenFlächenMannigfaltigkeiten

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.