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Geometry I:
Analytic and Projective Geometry
(Winter 2010)


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. timelike vectors should have scalar product 1 and spacelike 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 crossratio.
 [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 noneuclidean geometry: spherical, hyperbolic,
projective, Möbius, and Lie geometry. The continuation is
Geometry II: Discrete Differential Geometry.
Exercise sheets
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. SpringerVerlag, Berlin, 1968.

Wilhelm Blaschke. Projektive Geometrie. Birkhäuser, Basel, 1954.

Marcel Berger. Geometry. I & II. SpringerVerlag, Berlin, 1987.

Michèle Audin. Geometry. SpringerVerlag, Berlin, 2003.

H. S. M. Coxeter. NonEuclidean Geometry. Mathematical Association of
America, Washington, DC, 1998.
Office Hours
