Gäller från och med: Autumn 2018
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2018-10-08
Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: MATM23
Undervisningsspråk: 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.
Kunskap och förståelse
För godkänd kurs skall doktoranden
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.
Undervisningsform: Föreläsningar
Examinationsform: Muntlig tentamen
Betygsskala: Underkänd, godkänd
Examinator:
Kursansvariga: