MMG720 Differential Geometry Spring 25
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: 250604.pdf
Solutions: Sols250604.pdf
Exam: 250821.pdf
Solutions: Sols250821.pdf
Program
The schedule of the course is in TimeEdit.
Lectures
| Week | Sections | Contents | Lecture notes |
|---|---|---|---|
| 13-14 | 2.1-3 | Curve theory: introduction, different types of curves, arc length, curvature and torsion, Frenet formulae, fundamental thms. for plane and space curves, four-vertex thm and the isoperimetric inequality | Ch2_Curves.pdf |
| 15 & 17-18 | 3.1-8 | Classical surface theory: regular surfaces, smooth maps and diffeomorphisms, the tangent plane and the differential of a map, 1st and 2nd fundamental form, normal fields and orient ability, curvature, examples of classes of surfaces such as ruled surfaces and surfaces of revolution. | Ch3_ClassSurfaceTh.pdf |
| 19-20 | 4.1-7 | The inner geometry of surfaces: isometries, vector fields and covariant derivative, Christoffel symbols, Riemann curvature tensor, Gauss's eq. and Theorema Egregium, geodesics, the exponential map and special coordinate systems, parallel transport. | Ch4_Part1.pdf Ch4_Part2.pdf Ch4_Part3.pdf |
| 21 | 5.2 & 6.1-3 | Geometry, analysis and topology: variation of the metric, triangulations and the Gauss-Bonnet thm | Ch5.pdf GaussBonnet.pdf |
Recommended exercises
| Chapter | Exercises |
|---|---|
| 2 | 1, 4, 5, 7, 8, 11, 13, 16 |
| 3 | 2, 4, 6, 7, 10, 11, 18, 19, 23, 31, 32 |
| 4 | 2, 3, 5, 6, 7, 8, 11, 18, 19, 20, 22, 25, 26, 28 |
| 6 | 1, 2, 3, 5, 6 |
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 25/3 8:00 - Wednesday 9/4 17:00 |
| 2 | Thursday 24/4 8:00 - Friday 9/5 17:00 |
| 3 | Tuesday 13/5 8:00 - Wednesday 28/5 17:00 |
Course summary:
| Date | Details | Due |
|---|---|---|