Course Syllabus for

Riemannian Geometry

FMA160F, 7.5 credits

Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-10-08

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: MATM23
Teaching language: English


The aim of the course is to acquaint the postgraduate student with the basics of Riemannian geometry, in particular smooth manifolds of arbitrary finite dimensions, tangent bundles and Lie derivatives. The subject is an important field of research in mathematics, but methods from the subject are also important for mechanics -- where typically the phase space for a mechanical system is described by the tangent bundle of a nontrivial manifold -- and in the general theory of relativity.


Knowledge and Understanding

For a passing grade the doctoral student must

Course Contents

Differentiable Manifolds. The Tangent Space. The Tangent Bundle. Riemannian Manifolds. The Levi-Civita Connection. Geodesics. The Riemann Curvature Tensor. Curvature and Local Geometry.

Course Literature

Gudmundsson, S.: An Introduction to Riemannian Geometry. Centre for Mathematical Sciences, Lund University, 2017.
The participants should also consult some of the other books that are recommended on the course web page.

Instruction Details

Type of instruction: Lectures

Examination Details

Examination format: Oral exam
Grading scale: Failed, pass

Admission Details

Course Occasion Information

Contact and Other Information

Course coordinators:

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