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advanced_tools:connections:levi_civita_connection

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advanced_tools:connections:levi_civita_connection [2018/04/14 11:22]
aresmarrero ↷ Page name changed from advanced_tools:connections:christoffel_symbols to advanced_tools:connections:levi_civita_connection
advanced_tools:connections:levi_civita_connection [2021/08/23 02:30]
edi [Concrete]
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
-The Levi-Civita connection is a mathematical tool that we use to [[advanced_notions:​parallel_transport|parallel transport]] vectors around a manifold.+The Levi-Civita connection is a mathematical tool that we use to [[advanced_tools:​parallel_transport|parallel transport]] vectors around a manifold.
  
 Parallel transport is just the simplest way to compare vectors at different points in the manifold. Parallel transport is just the simplest way to compare vectors at different points in the manifold.
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 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/​|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