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Differential Geometry II (Winter 16)
– Analysis and geometry on manifolds –


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.
News
 There will be no lecture on 6 and 7 February. The homework can be turned in before the tutorial on 8 February.
 Corrected sign error in 1. exercise of the 6. sheet.
 Unfortunately, there are not enough participants to have two tutorials this semester. The tutorial on Thursday is thus cancelled.
Contents
Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.
Homework
 Exercise sheet 1, due 1 November
 Exercise sheet 2, due 8 November
 Exercise sheet 3, due 15 November
 Exercise sheet 4, due 22 November
 Exercise sheet 5, due 29 November
 Exercise sheet 6, due 6 December
 Exercise sheet 7, due 13 December
 Exercise sheet 8, due 10 January
 Exercise sheet 9, due 17 January
 Exercise sheet 10, due 24 January
 Exercise sheet 11, due 31 January
 Exercise sheet 12, due 7 February
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 50% of the homework assignments.
Material
Lecture notes:
The script is written parallel to the lecture. It can contain typos or even mistakes. If you have found some or you have comments please send an email to Felix.
Literature:
 Burstall, Basic Riemannian geometry in Spectral Theory and Geometry, L.M.S. Lect. Note Series 273, C.U.P. (1999), pages 129, [pdf]
 Petersen, Manifold theory, [essay]
 Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94, Springer
 Milnor, Topology from the Differentiable Viewpoint, U P Virginia
Further excellent notes on differential geometry can be found on Werner Ballmann's homepage.

Name 
Office hours 
Room 
email @math.tuberlin.de 
Lecturer 
Prof. Ulrich Pinkall 
by appointment  MA 822 
pinkall 
Assistant 
Felix Knöppel 
by appointment  MA 882 
knoeppel 
Secretary 
Beate Nießen 
TueThu 9.3011.30  MA 318 
niessen 
