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Differential Geometry II (Winter 17)
– 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
 The certificates can be picked up at Beate Niessen's office MA 318.
 There are no lectures on January 29/30. Homework can be handed in during the 29th at MA 882 or at the office MA 873
 The lecture on Tueday 17 October and the tutorial on Thursday 19 October both will take place at MA 144
Contents
Differentiable manifolds, vector bundles, differential forms, Riemannian geometry.
Homework
 Exercise sheet 1, due 30 October
 Exercise sheet 2, due 6 November
 Exercise sheet 3, due 13 November
 Exercise sheet 4, due 20 November
 Exercise sheet 5, due 27 November
 Exercise sheet 6, due 4 December
 Exercise sheet 7, due 11 December
 Exercise sheet 8, due 18 December
 Exercise sheet 9, due 8 January
 Exercise sheet 10, due 15 January
 Exercise sheet 11, due 22 January
 Exercise sheet 12, due 29 January
 Exercise sheet 13, due 5 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:
If you find mistakes or you have some 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 
