MATM13 Differential Geometry
is an alternatively compulsory course for a Master of Science degree in mathematics.
We show that a curve in R3 is, up to Euclidean motions, totally determined by its curvature and torsion. We study the second fundamental form of a surface, describing its shape in the ambient space R3. This leads to a fundamental object the curvature of the surface. Amongst many interesting results we prove the famous "Theorema Egregium" of Gauss which tells us that the curvature is an intrinsic object i.e. determined by the way we measure distances on the surface. Furthermore we prove the astonishing Gauss-Bonnet theorem. This implies that for a compact surface the curvature integrated over it is a topological invariant.Teaching
The teaching consists of lectures and seminars. Compulsory hand-in exercises may be given.Assessment
The module is assessed through a written and an oral examination.Course literature
Andrew Pressley, Elementary Differential Geometry, 2010.
Sigmundur Gudmundsson, An Introduction to Gaussian Geometry, 2013.Lecturer
Sigmundur Gudmundsson. You find all relevant information for the course at the lecturer's course page.Schedule
The schedule is available in the TimeEdit
schedule tool. For instructions on how to use TimeEdit click here