Manifolds

LECTURER: J. Larena

Prerequisites

Advanced Calculus. Real Analysis and Complex Analysis would be beneficial.

Topics

 

The aim of this course is to provide an introduction to differentiable manifolds with an eye on their relevance in modern theoretical physics. Nevertheless, no physics background is required.

Syllabus: Topological spaces; differentiable manifolds; calculus on manifolds; flows and Lie derivatives; differential forms; integration of differential forms; Lie groups and Lie algebras; action of Lie groups on manifolds; Riemannian and pseudo-Riemannian manifolds; parallel transport, connection and covariant derivative; curvature and torsion; Levi-civita connection; isometries; Killing vector fields; non-coordinate bases.

 

Textbooks

M. Nakahara, 'Geometry, topology and Physics', Graduate Student Series in Physics.

Tutorials

One tutorial per week.

Tests/Exams

Two tests and one final examination.

Last Modified: Tue, 28 Jan 2014 14:26:53 SAST