TU Berlin Fakultät II
Institut für Mathematik

Arbeitsgruppe Geometrie



Geometry Group







Differential Geometry II (Winter 15)

– Analysis and geometry on manifolds –

Lecture Prof. John Sullivan Mon08:30-10:00H 1029
Mon10:15-11:45H 1029
Tutorial Felix Knöppel Wed12:15-13:45MA 376
Thu12:15-13:45MA 841

This course is a BMS basic course and the lectures will be in English. Please feel free to ask any questions (and to turn in any work) in English or German.


  • Oral exams will be offered on Friday 20 May and on Friday 3 June.


Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.

Lecture Notes

Here is the revised 2015/6 version of Prof. Sullivan's lecture notes.

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

Note that 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. For reference, here are the lecture notes from last semester's course.



  • Kühnel, Differential Geometry / Differentialgeometrie, AMS / Vieweg
  • Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Ed, Academic Press
  • Bröcker and Jänich, Introduction 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

Homework should be turned in by groups of two students.

To get a certificate for the tutorial and qualify to take the oral exam at the end of the semester, you need to satisfactorily complete 60% of the homework assignments.

  Name Office hours Room email
Lecturer Prof. John Sullivan Thu 13:30–14:30MA 802 sullivan
Assistant Felix Knöppel by appointmentMA 882 knoeppel
Secretary Annett Gillmeister Mon, Tue, Thu, Fri 9:30–11:30MA 803 gillmeister

Felix Knöppel . 09.05.2016.