advanced_tools:connections:levi_civita_connection
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
advanced_tools:connections:levi_civita_connection [2018/04/14 13:51] theodorekorovin ↷ Links adapted because of a move operation |
advanced_tools:connections:levi_civita_connection [2023/04/02 03:28] edi [Concrete] |
||
|---|---|---|---|
| Line 13: | Line 13: | ||
| Parallel is necessary, for example, to define the covariant derivative. | Parallel is necessary, for example, to define the covariant derivative. | ||
| <tabbox Concrete> | <tabbox Concrete> | ||
| - | Christoffel symbols $\Gamma^i_{jk}$ are a particular type of connection that a Lorentzian manifold has (called the Levi-Civita connection). | + | Christoffel symbols $\Gamma^i_{jk}$ are a particular type of connection that a Lorentzian manifold has (called the Levi-Civita connection). |
| + | |||
| + | ---- | ||
| + | |||
| + | **Examples** | ||
| + | |||
| + | The diagram below shows three concrete examples for connections (Christoffel symbols) on simple 2-dimensional manifolds. For a more detailed explanation see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#metric_connect_curvature|Fun with Symmetry]]. | ||
| + | |||
| + | {{:advanced_tools:metric_connect_curvature.jpg?nolink}} | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
advanced_tools/connections/levi_civita_connection.txt · Last modified: 2023/04/02 03:28 by edi
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
