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Differential Geometry I
Differentialgeometrie I:
Kurven und Flächen (Sommer 2015)
Vorlesung 
Prof. John
Sullivan

Mo

1012 
MA 144 
Do

1012 
MA 144 
Übung 
Isabella Thiesen / Yun Hao

Mi 
1214 
MA 144 
Do 
1416 
MA 144 
This course will be taught in English.
Please feel free to ask questions in English or German
(at lectures and tutorials, via email, or at office hours).
News
13 July:
*
Oral exams will be offered on Tue 11 Aug, Thu 24 Sep and Tue 29 Sep.
(For those wishing to wait until after the start of WS, there will
be another date offered at the end of October.)
13 July:
*
Today's lecture will be the last one. Please fill out the
course
evaluation online.
9 July:
*
The last tutorial session was yesterday. Here
are the handwritten notes, a summary of surface theory.
30 June:
*
Homework 11 is now online. There will be
one more homework assignment next week.
29 June:
*
Here is the paper about classifying surfaces.
25 June:
*
The revised version of the lecture notes has more details about today's lecture.
22 June:
*
Homework 10 is now online, as are revisions to the lecture notes from today.
*
Oral exams for the course will be offered several times during the semester
break. Exact dates will be announced soon, but they will probably be during
the weeks of 10 August, 21 September and 28 September.
*
15 June:
*
Homework 9 is now online.
*
Of course there are two expansions of h_{12} = h_{21}
in terms of the shape operator and first fundamental form. In lecture today,
I started with the wrong one. I should have used
h_{12} =
h_{2}^{1}g_{11}
+ h_{2}^{2}g_{21}.
I have updated the lecture notes with a bit more detail here.
1 June:
*
There is an updated version of Sullivan's lecture notes
here with a few minor improvements.
If you find typos or other errors in the notes, please
report them via email.
29 May:
*
Homework 7 is now online.
27 May:
*
Homework 6 is now online.
18 May:
*
Yun Hao will be running the tutorials starting this week.
*
Prof. Sullivan will be at a conference, so there are
no office hours this week and Yun Hao will hold the Thursday lecture.
15 May:
* As there was no Thursday tutorial this week due to
the national holiday, you can find Isabella's notes for the last
tutorial here. * Here are some further references on exercise 3.2 if you are interested: https://archive.org/details/kreisundkugel00blasgoog (p.161) http://www.ams.org/mathscinetgetitem?mr=10992 (Rather short proof using Moebius geometry)
8 May:
* In the
Thursday tutorial there was a question about the isoperimetric
inequality for selfintersecting curves. For those who were missing a
reference for that case can read further here (p.1185 middle):
http://www.ams.org/journals/bull/19788406/S000299041978145534/S000299041978145534.pdf
* Here is
the promised hint for ex. 3.2: Set up a
proof by contradiction, and follow our proof of the
fourvertex theorem. If you need to, you may assume that the
points of intersection lie in no semicircle.
* We are
happy to announce that we found a tutor for the second part of the
semester. From next week on, Yun Hao will take over the tutorials. It
would be great if you could all hand in your homework from now in
English!
30 Apr:
Remark to ex.2 on sheet 2:
The involute is
not unique; in fact there is a oneparameter family of involutes. The
exercise is still valid though :).
28.Apr:
Please find a corrected
version of exercise
sheet 2 below. There was a wrong problem formulation in ex. 4. Sorry
for that!
 21 Apr:
 The first (short) homework assignment is posted below and
due 27 April.
In the future, we will try to post assignments at least 10 days in
advance.
 21 Apr:
 Homework will be due on Mondays at the beginning of
lecture.
Homework assignments are to be turned in by groups of 2 students.
 21 Apr:
 Isabella Thiesen will serve as assistant for the course
for the first part of the semester.
Tutorials will indeed start
this Wednesday and Thursday (2223 April).
Topics
Differential geometry of smooth curves and surfaces in two
and threedimensional euclidean space.
Homework
Homework assignments will be due each Monday at the beginning of
lecture;
they are to be turned in by groups of two students.
To get the Übungsschein, you need to get at least 60% of the points
on the homework (on average over the course of the semester).
 Assignment 1, due 27 April
 Assignment 2 (corrected),
due 4 May
 Assignment 3, due 11 May
 Assignment 4, due 18 May
 Assignment 5, due 28 May
 Assignment 6, due 1 June
 Assignment 7, due 8 June
 Assignment 8, due 15 June
 Assignment 9, due 22 June
 Assignment 10, due 29 June
 Assignment 11, due 6 July
 Assignment 12, due 13 July
Lecture Notes
Sullivan's lecture notes from Summer 2013 are available
here.
A revised version with a few improvements is now here.
Recommended Textbooks
 Blaschke & Leichtweiß. Elementare
Differentialgeometrie
 Do Carmo. Differential Geometry of Curves and
Surfaces
 Hilbert & CohnVossen. Anschauliche
Geometrie
 Hopf. Differential Geometry in the Large
 Kühnel. Differentialgeometrie
 McCleary. Geometry from a Differentiable Viewpoint
 Montiel & Ros. Curves and Surfaces
 Struik. Lectures on Classical Differential Geometry
