Differential Geometry
Differentialgeometri

MATM13F, 7.5 credits

Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-08-24

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATM13
Teaching language: English

Aim

The aim of the course is to give the graduate student good knowledge about important concepts for the mathematical description of smooth two dimensional surfaces in space.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to account for basic concepts of differential geometry such as principal curvatures, Gaussian curvature, mean curvature and, geodesics.
• be able to explain how the principal curvatures in a point determine the local shape of the surface near the point.
• be able to explain how knowledge about how the Gaussian curvature varies over the surface gives information about the global form of the surface.

Course Contents

Geometry for hypersurfaces in Euclidean spaces. The Gauss map, curvature, focal points, minimal surfaces, convex surfaces, the Gauss-Bonnet theorem in two dimensions.

Course Literature

Gudmundsson, S.: An Introduction to Gaussian Geometry. Centre for Mathematical Sciences, Lund University, 2017.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

Examination formats: Written exam, oral exam, written assignments. Compulsory assignments may occur.
Grading scale: Failed, pass
Examiner:

Admission Details

Admission requirements: At least 60 hp mathematics.
Assumed prior knowledge: Calculus in several variables including vector analysis in three dimensions.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: http://www.matematik.lu.se/matematiklu/personal/sigma/MATM/Gaussian-Geometry.htmll