Add a new page:
Sidebar
advanced_tools:connections:levi_civita_connection
This is an old revision of the document!
$ \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)$
Levi-Civita connection
also known as Christoffel Symbols; see also connections
Intuitive
The Levi-Civita connection is a mathematical tool that we use to parallel transport vectors around a manifold.
Parallel transport is just the simplest way to compare vectors at different points in the manifold.
Parallel is necessary, for example, to define the covariant derivative.
Concrete
Christoffel symbols $\Gamma^i_{jk}$ are a particular type of connection that a Lorentzian manifold has (called the Levi-Civita connection).
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
The Christoffel symbols appear in the most important equations of general relativity: the Einstein equation and the geodesic equation.
advanced_tools/connections/levi_civita_connection.1523697739.txt.gz · Last modified: 2018/04/14 09:22 (external edit)
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
