Fakultät II
Institut für Mathematik

# Arbeitsgruppe Geometrie

Geometry Group

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# Geometry I: Analytic and Projective Geometry

## (Winter 2010)

Lecture Tutorial Alexander Bobenko Mon 14-16 MA 313 Thu 14-16 MA 313 Thilo Rörig Wed 10-12 MA 651 Thu 10-12 MA 642

This is a course of the Berlin Mathematical School held in English.

### News

[24.01.]
Exercise 11.1. The vectors in the given equation must be normalized to satisfy them, i.e. time-like vectors should have scalar product -1 and space-like vectors +1 to satisfy the distance formulas.
[20.01.]
There is an article by Charles A. Rupp "Stereographic Projection of a Quadric", American Mathematical Monthly, Vol. 35, No. 8 (Oct. 1928) on Brianchon and Pascal Theorems on a quadric. I have a copy of the article in my office for those who are interested.
[10.01.]
Ex. 9.3. Due next week.
[09.01.]
Ex. 9.1. Removed some imprecision. See updated version below.
[16.12.]
Merry Christmas and a Happy New Year!
[14.12.]
Error in ex. 7.3: The order of the points has to be changed from cr(Q,R,A,B) to cr(Q,A,R,B), see corrected sheet below. Sorry. If you need more time to solve the exercise now, you may hand it in with the next sheet.
[30.11.]
No tutorials this week (1./2.12.) due to illness. Nevertheless there is an exercise sheet.
[22.11.]
No lecture today.
[16.11.]
The rooms for thursdays tutorial changed and is from now on in MA 642
[03.11.]
I created a blog for the geometry course. Please read, subscribe, comment, or write stuff you are thinking about concerning the geometry class. I started it today because of a nice and lively discussion in my tutorial about projective transformations and cross-ratio.
[28.10.]
Finally the rooms are fixed. See above schedule. Sorry for the inconvinience.
[05.10.]
Lecture starts on monday 18.10. at 14h at MA 650.

### Contents

Euclidean and non-euclidean geometry: spherical, hyperbolic, projective, Möbius, and Lie geometry. The continuation is Geometry II: Discrete Differential Geometry.

### Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

### Literature

• Lecture notes by Boris Springborn
• V. V. Prasolov & V. M. Tikhomirov. Geometry. Translations of Mathematical Monographs, 200. American Mathematical Society, Providence, RI, 2001.
• Nigel Hitchin's lecture notes on Projective Geometry.
• Felix Klein. Vorlesungen über höhere Geometrie. Grundlehren der Mathematischen Wissenschaften, 22. Springer-Verlag, Berlin, 1968.
• Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.
• Marcel Berger. Geometry. I & II. Springer-Verlag, Berlin, 1987.
• Michèle Audin. Geometry. Springer-Verlag, Berlin, 2003.
• H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, Washington, DC, 1998.

### Office Hours

 Office hours Alexander Bobenko Tuesday 14-15h MA 881 Thilo Rörig Monday 11-13h MA 874

 Thilo Rörig . 02.02.2011.