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Differential Geometry II (Winter 19)

– Analysis and geometry on manifolds –


Lecture Prof. John Sullivan Thu14:00-16:00MA 841
Thu16:00-18:00MA 841
Tutorial Chris Savva Tue14:00-16:00MA 841
Wed10:00-12:00MA 376

This course is a BMS basic course and the lectures will be in English. Please feel free to ask any questions during lectures in English or German. Homework should be submitted in English.


News

[2020, Feb 3]
Exams will be offered on the following days: 13, 14, 24 and 26 February, as well as in the week of 30 March – 3 April.
[2020, Feb 3]
There will be no lecture on 13 February.
[2020, Jan 30]
Exercise Sheet 13 is now posted. This is the last Exercise Sheet.
[2020, Jan 14]
The week of 20-24.1.2020 there will be a tutorial only on Wednesday 22.1.2020. The tutorial of Tuesday 21.1.2020 is cancelled. Office hours for Chris for the week of 20-24.1.2020 will be by appointment.
[2020, Jan 14]
Office hours for Chris on Wednesday (15.1.2020) are cancelled.
[2020, Jan 6]
This week (9.1.2020) there will only one lecture 14:15–15:45.
[2019, Nov 19]
Office hours for Chris on Wednesday (20.11.2019) are cancelled. Instead, there will be office hours on Friday (22.11.2019) 14:00-15:00.
[2019, Nov 15]
Exercise Sheet 5 is now posted. Make sure to check the current version since there was a mistake when initially posted.
[2019, Oct]
Exersise Sheet 3 is now posted. Updated office hours for Chris.
[2019, Oct]
Exersise Sheet 2 is now posted. On the Exercise Sheet 1, Exercise 3 is updated as already discussed.
[2019, Oct]
The first lecture is on Thursday, October 17. Tutorials start the second week on October 22 and 23.

Contents

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

Lecture Notes

Updated lecture notes as of 3 February.

These lecture notes will be further updated as the semester progresses. Please email Prof. Sullivan with any suggestions for corrections or improvements! For comparison, here is the version from Winter 2015/16.

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 Prof. Sullivan's lecture notes from last semester.

Homework

Literature

  • 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 (in English).
  • Homework is due weekly at the beginning of the lecture on Thursday.
  • To get a certificate for the tutorial and qualify to take the oral exam at the end of the semester, you need to get at least 60% of the points on the homework assignments.
  Name Office hours Room email
@math.tu-berlin.de
Lecturer Prof. John Sullivan TBAMA 802 sullivan
Assistant Chris Savva Tue 16:00–17:00, Wed 12:00–13:00MA 804 savva
Secretary Heather Heintzel Mon-Fri 08:45–11:45MA 801 heintzel

Chris Savva . 04.02.2020.
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