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. 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

[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.

Exercise sheets

• Sheet 01 due 03/04 Nov 10
• Sheet 02 due 10/11 Nov 10
• Sheet 03 due 17/18 Nov 10
• Sheet 04 due 24/25 Nov 10
• Sheet 05 due 01/02 Dec 10
• Sheet 06 due 08/09 Dec 10
• Sheet 07 due 15/16 Dec 10
• Sheet 08 due 5/6 Jan 11
• Sheet 09 due 12/13 Jan 11
• Sheet 10 due 19/20 Jan 11
• Sheet 11 due 26/27 Jan 11
• Sheet 12 due 02/03 Feb 11
• Sheet 13 due 09/10 Feb 11

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