TU Berlin Fakultät II
Institut für Mathematik

Arbeitsgruppe Geometrie



Geometry Group



Vergangene Semester


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       Differential Geometry I

Differentialgeometrie I:
Kurven und Flächen (Sommer 2015)

Vorlesung Prof. John Sullivan
10-12 MA 144
10-12 MA 144
Übung Isabella Thiesen / Yun Hao
Mi 12-14 MA 144
Do 14-16 MA 144

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).


13 July:
        * Oral exams will be offered on Tue 11 Aug, Thu 24 Sep and Tue 29 Sep. (For those wishing to wait until after the start of WS, there will be another date offered at the end of October.)
13 July:
        * Today's lecture will be the last one. Please fill out the course evaluation online.
9 July:
        * The last tutorial session was yesterday. Here are the handwritten notes, a summary of surface theory.
30 June:
        * Homework 11 is now online. There will be one more homework assignment next week.
29 June:
        * Here is the paper about classifying surfaces.
25 June:
        * The revised version of the lecture notes has more details about today's lecture.
22 June:
        * Homework 10 is now online, as are revisions to the lecture notes from today.
        * Oral exams for the course will be offered several times during the semester break. Exact dates will be announced soon, but they will probably be during the weeks of 10 August, 21 September and 28 September.
15 June:
        * Homework 9 is now online.
        * Of course there are two expansions of h12 = h21 in terms of the shape operator and first fundamental form. In lecture today, I started with the wrong one. I should have used h12 = h21g11 + h22g21. I have updated the lecture notes with a bit more detail here.
1 June:
        * There is an updated version of Sullivan's lecture notes here with a few minor improvements. If you find typos or other errors in the notes, please report them via email.
29 May:
        * Homework 7 is now online.
27 May:
        * Homework 6 is now online.
18 May:
        * Yun Hao will be running the tutorials starting this week.
        * Prof. Sullivan will be at a conference, so there are no office hours this week and Yun Hao will hold the Thursday lecture.
15 May:
        * As there was no Thursday tutorial this week due to the national holiday, you can find Isabella's notes for the last tutorial here.
        * Here are some further references on exercise 3.2 if you are interested:
            https://archive.org/details/kreisundkugel00blasgoog (p.161)
                http://www.ams.org/mathscinet-getitem?mr=10992 (Rather short proof using Moebius geometry) 
8 May:
        * In the Thursday tutorial there was a question about the isoperimetric inequality for self-intersecting curves. For those who were missing a reference for that case can read further here (p.1185 middle):
        * Here is the promised hint for ex. 3.2: Set up a proof by contradiction, and follow our proof of the four-vertex theorem.  If you need to, you may assume that the points of intersection lie in no semicircle.        
        * We are happy to announce that we found a tutor for the second part of the semester. From next week on, Yun Hao will take over the tutorials. It would be great if you could all hand in your homework from now in English!
30 Apr:
          Remark to ex.2 on sheet 2: The involute is not unique; in fact there is a one-parameter family of involutes. The exercise is still valid though :-).

          Please find a corrected version of exercise sheet 2 below. There was a wrong problem formulation in ex. 4. Sorry for that!
21 Apr:
The first (short) homework assignment is posted below and due 27 April.
In the future, we will try to post assignments at least 10 days in advance.
21 Apr:
Homework will be due on Mondays at the beginning of lecture.
Homework assignments are to be turned in by groups of 2 students.
21 Apr:
Isabella Thiesen will serve as assistant for the course for the first part of the semester.
Tutorials will indeed start this Wednesday and Thursday (22-23 April).


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


Homework assignments will be due each Monday 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).

Lecture Notes

Sullivan's lecture notes from Summer 2013 are available here. A revised version with a few improvements is now 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
  Name Sprechstunde Raum email
Dozent Prof. John Sullivan Do, 13:30-14:30 Uhr
MA 802
Assistent Yun Hao
Do, 16-18 Uhr
MA 216 hy_haoyun@163.com
Sekretariat Annett Gillmeister Mo, Di, Do, Fr 9:30 - 11:30 Uhr MA 803 gillm@math.tu-berlin.de

John Sullivan . 14.07.2015.