Geometry II (Summer 2019)

This is a basic course of the Berlin Mathematical School and lectures will be held in English.

News

[2.7.]

Isabella cannot offer office hours on Thursday 3rd but two office hours next week: Monday 8th, 11-13, and Thursday,11th, 11-13. Isabella is out of office from July 15th to August 3rd, after that office hours by appointment. Also, if you cannot make it to the office hours next week but have some (urgent) questions please send an email for an appointment.

[20.6.]

The tutorial on Wednesday, July 3rd, 14:00-16:00 will be replaced by one on Tuesday, July 2nd, 12:00-14:00 in MA 313/314.

[18.6.]

Isabella's office hour changed to Thursday, 11:00-13:00.

[5.6.]

Isabella's office hour this week is exceptionally on Thursday, 11:00-13:00.

[30.5.]

And one more correction in Homework 7: In Ex.1, the first two signatures must be interchanged (corrected version online).

[29.5.]

Please note the small correction in Homework 7, Ex.3 in the definition of the Quadric.

[21.5.]

For details about the classification of  Möbius transformations and pencils of circles see also the book by Keen, Lakic, Hyperbolic geometry from a local viewpoint (Chap 1.5.1.) (not in the library but you can ask Isabella for a copy)

[21.5.]

Due to illness, there will be no tutorial sessions this week, and Isabella's office hour has to be cancelled.

[10.5.]

In Homework 4, Ex 2.2 there is a tiny error, please replace |c| by |m|.

[26.4.]

Starting April 30th, the tutorial on Wednesday morning will be moved to Tuesday morning. As May 1st is a holiday, everyone is welcome to join the Tuesday morning tutorial on April 30th.

[12.4.]

The first homework is online (see below under "Exercise sheets").
You can find all books that are listed under references (and are not available online) in the math library on the first floor, in the "Semesterapparat" of this course (shelf behind the counter). Please note that these books can only be used in the library.

[3.4.]

Tutorials will start in the second week of the semester (April 17th).

Contents

• Non-Euclidean geometries and Klein's Erlangen program:
  • projective geometry (continued from Geometry I)
  • hyperbolic, spherical and Euclidean geometry (revisited)
  • Möbius-, Laguerre- and Lie-Geometry
• Aspects of Discrete Differential Geometry

Literature

• Springborn, old (but partially updated) lecture notes from the 2007 version of the course "Geometry I" at TU Berlin
• Euclid, Elements: online with java or Greek beside English text
• Prasolov & Tikhomirov, Geometry, TMM 200, Amer. Math. Soc.
• Hitchin, lecture notes on Projective Geometry: Chapters 1&2 (Intro, Proj. Spaces),   3 (Quadrics),   4 (Exterior Algebra),   5 (Klein's Erlanger Program)
• Fuchs & Tabachnikov, Mathematical Omnibus
• Klein, Vorlesungen über höhere Geometrie, GMW 22, Springer
• Blaschke, Projektive Geometrie, Birkhäuser
• Berger, Geometry I & II, Springer
• Audin, Geometry, Springer
• Coxeter, Non-Euclidean Geometry, Math. Assoc. Amer.
• Cannon, Floyd, Kenyon & Parry, Hyperbolic Geometry, from Flavors of Geometry, MSRI
• Martin, The Foundations of Geometry and the Non-Euclidean Plane, UTM, Springer
• Henderson, Experiencing Geometry, Prentice Hall
• Blaschke, Thomsen: Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. III, Differentialgeometrie der Kreise und Kugeln, 1929
• Cecil, Lie Sphere Geometry: With Applications to Submanifolds
• Elie Cartan, Theory of Spinors.

Exercise sheets

•       Exercise 1, due 23.4.
  
•       Exercise 2, due 30.4.
•       Exercise 3, due 7.5.
•       Exercise 4, due 14.5.
•       Exercise 5, due 21.5.
•       Exercise 6, due 28.5.
•       Exercise 7, due 4.6.
•       Exercise 8, due 11.6.
•       Exercise 9, due 18.6.
•       Exercise 10, due 25.6.
•       Exercise 11, due 2.7.

Homework policy and exam information

• To get a certificate for the tutorial and thus qualify to take the oral exam, you need to satisfactorily complete 60% of the homework assignments.
• The exercises are to be handed in in groups of two people.
• The homework is due weekly on Tuesday before the lecture. 

Office Hours