TU Berlin Fakultät II
Institut für Mathematik

Arbeitsgruppe Geometrie



Geometry Group



Vergangene Semester


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       Differential Geometry I

Differential Geometry I:
Curves and Surfaces (Summer 2019)

Lecture Prof. John Sullivan
10:15–11:45 MA 841
10:15–11:45 MA 841
Tutorial Max Krause
Mon 16:15–17:45 MA 841
Wed 16:15–17:45 MA 851

This course will be taught in English.
Please feel free to ask questions in English or German (at lectures and tutorials, via email, or at office hours).


  • The tutorial on Wednesday, July 10, is cancelled due to sickness.
  • There is an newly updated version of the lecture notes available below.
  • Oral exams will be offered 10-11 July and 20-23 August (and also in November).
  • Max's office hours on July 4 are cancelled, there will instead be office hours on July 3 from 10-12.
  • There will be a total of 11 homework sheets worth 20 points each, with the final one being due on July 5.
  • Exercises 2 and 4 on sheet 6 have been updated. For 2, you should assume that U is path-connected. Exercise 4 also gets a connectedness condition.
  • Due to the public holiday on May 30, Max's office hours for that week will be on Wednesday, May 29, from 1-2pm.
  • Please note the room change for the Wednesday tutorial. It will from now on take place in MA851.
  • The tutorial session on April 24 is cancelled.
  • The first exercise sheet will be due on April 26, to account for Easter holidays. There will be no lectures or tutorials on April 19 as well as April 22.


Differential geometry of smooth curves and surfaces in two- and three-dimensional euclidean space.


Homework assignments will be due each Friday at the beginning of lecture; they are to be turned in by groups of two students.
To get the Übungsschein, you need to get at least 60% of the points on the homework (on average over the course of the semester). This amounts to a total of 132 points.

Lecture Notes

An updated version of the lecture notes is now available here. Sullivan's lecture notes from Summer 2015 are available here.

Recommended Textbooks

  • Blaschke & Leichtweiß. Elementare Differentialgeometrie
  • Do Carmo. Differential Geometry of Curves and Surfaces
  • Hilbert & Cohn-Vossen. Anschauliche Geometrie
  • Hopf. Differential Geometry in the Large
  • Kühnel. Differentialgeometrie
  • McCleary. Geometry from a Differentiable Viewpoint
  • Montiel & Ros. Curves and Surfaces
  • Struik. Lectures on Classical Differential Geometry
These books are also listed in Primo.

Contact Information

  Name Office hours Room email
Lecturer Prof. John Sullivan TBA
MA 802
Assistant Max Krause
Thu 13:15–14:45
MA 804 m.krause@tu-berlin.de
Secretary Heather Heintzel Mon–Fri 8:45–11:45 MA 801 heintzel@math.tu-berlin.de

John Sullivan . 10.07.2019.