# 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 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

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

## 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.