TU Berlin Fakultät II
Institut für Mathematik

Arbeitsgruppe Geometrie



Geometry Group



Vergangene Semester


Images, Videos, and Games

Virtual Math Labs




Differential Geometry II:   Manifolds (Winter 2013–2014)

Lecture Prof. Dr. John Sullivan
8:30-10:00 MA 313
10:15-11:45 MA 313
Tutorial Isabella Thiesen
Tu 16:00-17:30 MA 212
Wed 12:30-14:00 MA 650

This course is a BMS basic course and the lectures will be in English.
Please feel free to ask any questions in English or German (during the course, via email, or at office hours).


10.4. Exams will be offered on 29 April. See Prof. Sullivan's webpage for details.

11.2. Exams will be offered on 14 February, 13 March and 10 April. See Prof. Sullivan's webpage for details.

10.2. Complete lecture notes now online.

4.2. The 12th exercise sheet is online

27.1. The 11th exercise sheet is online

20.1. The 10th exercise sheet is online. There will be 2 more, with the 12th one being optional.

13.1. The 9th exercise sheet is online

6.1. The 8th exercise sheet is online

13.12. Homework 7, ex 2: The metric g on M seems to be missing a factor 4.
           There will be NO TUTORIALS NEXT WEEK (December 17/18th).

10.12. Homework 7 corrected (Def. of f in ex.2 was wrong)

9.12. The 7th exercise sheet is online

8.12. Of course the formula in problem 3(a) on homework 6 should be the same as in the lecture notes: [fX,gY]= fg[X,Y]+ f(Xg)Y - g(Yf)X

5.12. The next lecture (9.12.) will be in room MA 313 (as usual).

28.11. The sixth exercise sheet is online

18.11. The fifth exercise sheet is online

15.11. In ex. 2 on ex. sheet 3 the dimension of M is m=n.

11.11. The fourth exercise sheet is online

06.11. Homework 3 corrected (ex.2, 3)

05.11. The third exercise sheet is online

30.10. Small notational change in exercise 2.

28.10. The second exercise sheet is online.

21.10. The tuesday tutorial will be from 16:00-17:30 in MA 212. The first exercise sheet is online.

09.09. The tutorials start in the second week (October 22nd).


Differentiable manifolds, Vector bundles, Differential forms, Riemannian geometry.

The course Differential Geometry I (Curves and Surfaces) is not strictly a prerequisite for this course. It gives useful geometric insight on the lower dimensional cases but is logically independent – the courses can be taken in either order.

Lecture Notes

Please email Prof. Sullivan with any suggestions for corrections or improvements to these lecture notes.



    • Kühnel, Differential Geometry / Differentialgeometrie, AMS / Vieweg
    • Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press
    • Bröcker and Jänich, Intro to Differential Topology / Einführung in die Differentialtopologie, CUP / Springer
    • Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer
    • Morgan, Riemannian Geometry: A
    • Beginner's Guide, 2nd Ed, A K Peters
    • Bishop and Goldberg, Tensor Analysis on Manifolds, Dover
    • Milnor, Topology from the Differentiable Viewpoint, U P Virginia
    • Spivak, Calculus on Manifolds, Benjamin/Cummings
    • Sharpe, Differential Geometry, GTM 166, Springer

    Homework policy

    To get a certificate for the tutorial, you need to satisfactorily complete 60% of the homework assignments. Homeworks are to be prepared in groups of two students and are due at the beginning of the Monday lectures.

      Name Office hours
    Room email
    Lecturer Prof. Dr. John Sullivan Tue 11:30–12:30
    MA 802
    Assistant Isabella Thiesen
    Wed 15–17
    MA 866 thiesen@math.tu-berlin.de
    Secretary Annett Gillmeister Mon, Tue, Thu, Fri 9:30–11:30 MA 803 gillm@math.tu-berlin.de

    Isabella Thiesen . 10.04.2014.