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DGI
Differential Geometry II: Manifolds (Winter 2013–2014)
Lecture 
Prof. Dr. John
Sullivan

Mo

8:3010:00 
MA 313 
Mo

10:1511:45 
MA 313 
Tutorial 
Isabella Thiesen

Tu 
16:0017:30 
MA 212

Wed 
12:3014:00 
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).
News10.4. 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 16:0017:30 in MA 212. The first exercise sheet is online.
09.09. The tutorials start in the second week (October 22nd).
ContentsDifferentiable 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.
Homework
Literature
 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.
