MMG720 Differential Geometry Spring 23

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This page contains the program of the course: lectures, exercise sessions and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

A summary of important concepts and results from the course can be found here: Important concepts and results

Exam: 240104.pdf
Solutions: Sols240104.pdf

Exam: 230814.pdf
Solutions: Sols230814.pdf

Exam: 230531.pdf
Solutions: Sols230531.pdf

Program

The schedule of the course is in TimeEdit.

Lectures

Week Section Contents Lecture notes
12 1.1-1.5, 2.1-2.3 Introduction, regular curves, arc length, Frenet-Serret trihedron, curvature and torsion Chapter1.pdf 
Chapter2.pdf
13 3.1-3.3 Isoperimetric inequality, four vertex theorem Chapter3.pdf
16 4.1-4.5, 5.1-5.3, 5.6 Regular surfaces, examples, tangent plane  
17 6.1-6.4, 7.1-7.3 First fundamental form, isometries, conformal maps, area, Gauss map, second fundamental form, normal curvature Chapter6.pdf
Chapter7.pdf
18 8.1-8.4 Gaussian and mean curvature, constant curvature Chapter8.pdf
19 9.1-9.5 Geodesics, geodesics as shortest path Chapter9.pdf
20-21 10.1-10.4, 13.1-13.4 Theorema egregium, Mainardi-Codazzi equations, Gauss-Bonnet theorem Chapter10.pdf
Chapter13.pdf

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Recommended exercises

Week Exercises
12 1.1.1-5, 1.1.7, 1.2.1, 1.2.3-4, 1.3.1i,ii, 2.1.1i.ii,iv
13 1.4.1, 2.1.2, 2.2.2, 2.3.1, 3.1.1, 3.3.3, 3.3.2
16 4.1.1-4, 4.2.3, 4.2.5, 4.4.1, 4.4.3, 5.1.2
17 6.1.1ii,iv, 6.2.2-3, 6.3.3-4, 7.1.1, 7.3.1-3
18 7.3.6-7, 8.1.1, 8.1.8-9, 8.2.2-3
19 8.2.7-8, 8.3.1i, 9.1.1, 9.2.1-, 9.3.1-2
20-21 9.1.5, 9.2.2, 9.5.1-2, 10.2.5, 10.1.1-2, 13.1.1

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Homework

There will be three sets of homework, with each set giving a maximum of 4 points towards the final grade, see Course PM. The homework will be available as assignments in Canvas during the following periods.

Homework Available
1 Tuesday 21/3 8:00 - Wednesday 5/4 17:00
2 Tuesday 18/4 8:00 - Wednesday 3/5 17:00
3 Tuesday 9/5 8:00 - Friday 26/5 17:00

Course summary:

Course Summary
Date Details Due