# MMG720, Differential Geometri, Spring 19

## Latest news

Solutions to the reexams on 190823 and 200108 are posted under documents at the activity of the course in GUL.

Solutions for the exam.

Welcome to the course! The schedule for the course can be found in TimeEdit.

## Teachers

Course coordinator:
Jan Stevens
room H5028, Tel. 772 5345, e-mail: stevens(at)chalmers(dot)se

## Course literature

Andrew Pressley, Elementary Differential Geometry , Springer, London etc., 2nd ed, 2010.

Gauss' Theorema Egregium

Reference literature:
M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976
Chr. Bär, Elementary Differential Geometry , Cambridge University Press, 2010.
L. M. Woodward and J. Bolton, A First Course in Differential Geometry: Surfaces in Euclidean Space. Cambridge University Press, 2018

## Program

#### Lectures

Days
Section
Contents
25 & 28/3
1.1-1.5, 2.1-2.3
Introduction, regular curves, arc length, Frenet-Serret trihedron, curvature and torsion
1 & 4/4
3.1-3.3
Isoperimetric inequality, four vertex theorem
8 & 11/4
4.1-4.5, 5.1-5.3, 5.6
Regular surfaces, examples, tangent plane
29/4, 2/5
6.1-6.4, 7.1-7.3
First fundamental form, isometries, conformal maps, area, Gauss map, second fundamental form, normal curvature
6 & 9/5
8.1-8.4
Gaussian and mean curvature, constant curvature
13 & 16/5
9.1-9.5
Geodesics, geodesics as shortest path
20 & 23/5
10.1-10.4, 13.1-13.4
Theorema egregium, Mainardi-Codazzi equations, Gauss-Bonnet theorem

#### Recommended exercises

Day
Exercises
29/3
1.1.1-3, 1.1.5, 1.1.7, 1.2.1, 1.2.3, 1.3.1, 1.4.1
5/4
2.1.1-2, 2.2.2, 2.3.1, 3.1.1, 3.3.2
12/4
4.1.1-4, 4.2.5, 4.4.1, 4.4.3, 5.1.2
3/5
6.1.1ii,iv, 6.2.2-3, 6.3.3-4
10/5
7.1.1, 7.3.2., 7.3.6-7, 8.1.1, 8.1.8-9
17/5
8.2.3, 8.2.7-8, 8.3.1i, 9.1.1, 9.1.5
24/5
9.2.1-2, 9.3.1-2, 10.1.1-2, 10.2.5

## Course requirements

The learning goals of the course can be found in the course plan.

## Homework

• Homework 1. To be handed in at the latest Thursday April 4 at the end of the lecture
• Homework 2. To be handed in at the latest Monday April 29
• Homework 3. To be handed in at the latest Thursday May 9
• Homework 4. To be handed in at the latest Thursday May 23

## Examination

The final exam is a written exam (no aids allowed) with 6 questions, which give together 25 points. For a pass (G) you need 12 points and for a pass with distinction (VG) you need 18 points.
The exam takes place on Wednesday June 5, in the afternoon (14-18).
There will be four possibilities to hand in homework. The homework can give up to two bonus points, which can be used at the exam (but not at re-exams) to reach a pass; for a pass with distinction the bonus points count only half.

## Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.