Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-10-08
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
Differentiable Manifolds. The Tangent Space. The Tangent Bundle. Riemannian Manifolds. The Levi-Civita Connection. Geodesics. The Riemann Curvature Tensor. Curvature and Local Geometry.
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.
Type of instruction: Lectures
Examination format: Oral exam
Grading scale: Failed, pass