*Course Syllabus for*
# 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.

**Types of instruction:** Lectures, seminars

**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

**Course coordinators:**

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