Differential Geometry

Teaching semester

Irregular. The course is offered spring 2021

Objectives and Content

The course gives an introduction to the techniques of differential geometry. In particular we will study connections and curvature of smooth manifolds. Further topics may wary, for example the course can cover homogeneous spaces, Lie groups, semi-Riemannian geometry and general relativity theory.

Learning Outcomes

After completed course, the students are expected to be able to:

• Explain the central topics of curvature, connection and Riemannian metric.
• Compute the curvature of spheres and hyperbolic spaces.
• Explain the relationship between distances and geodesic curves
• Computer curvature in local coordinates.

Recommended Previous Knowledge

MAT121 Linear Algebra, MAT212 Functions of Several Variables, and MAT243 Manifolds

Forms of Assessment

Oral examination

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.