Differential Geometry I Autumn 2017

Prof. Dr. Dietmar A. Salamon
Charel Antony and Samuel Trautwein
Mo 10-12 HG G5, Wed 13-15 HG G5


Topology and Analysis II. See Chapters 3 (Implicit Function Theorem), 4 (Flow of Vector Fields) and Appendices A,B,C (Basic Topology) of these German lecture notes: here. For topology, you can also see the standard reference by Munkres.

Lecture Notes

Lecture Notes will be updated over the semester. The most up to date version can be found here. If you spot any typos, please communicate these to the lecturer.

Short Description

Submanifolds of \(\mathbb{R}^n\), tangent bundle, embeddings and immersions, vector fields, Lie bracket, Frobenius' Theorem. Geodesics, exponential map, completeness, Hopf-Rinow. Levi-Civita connection, parallel transport, motions without twisting, sliding, and wobbling. Isometries, Riemann curvature, Theorema Egregium. Cartan-Ambrose-Hicks, symmetric spaces, constant curvature, Hadamard's theorem.

The new exercises will be posted here on Tuesday. We expect you to look at the problems before exercise class and to prepare questions for the exercise class on Thursday/Friday.

If you want to hand in your solutions, please do so by the following Monday at 14:00 in your assistant's box in HG F28. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG F28. Note that model solutions will be provided.

If you spot any mistakes or typos in the exercises or solutions, please communicate these to the coordinators.

exercise sheet due by solutions
Exercise sheet 1 September 25 Solutions 1
Exercise sheet 2 October 2 Solutions 2
Exercise sheet 3 October 9 Solutions 3
Exercise sheet 4 October 16 Solutions 4
Exercise sheet 5 October 23 Solutions 5
Exercise sheet 6 October 30 Solutions 6
Exercise sheet 7 November 6 Solutions 7
Exercise sheet 8 November 13 Solutions 8
Exercise sheet 9 November 20 Solutions 9
Exercise sheet 10 November 27 Solutions 10
Exercise sheet 11 December 4 Solutions 11
Exercise sheet 12 December 11 Solutions 12
Exercise sheet 13 December 18 Solutions 13
Exercise sheet 14 Merry Christmas and a Happy New Year :)

Please sign up to an exercise class on echo ( echo.ethz.ch ).

Th 14-15HG D 5.2Charel Antonyen
Th 14-15HG E 21Samuel Trautweinen
Th 15-16HG D 7.2Charel Antonyen
Fr 13-14HG G 26.3Samuel Trautweinen

We will add books here that complement the material in class.