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advanced_tools:connections:levi_civita_connection [2018/04/14 11:22] aresmarrero ↷ Page moved from advanced_notions:general_relativity:christoffel_symbols to advanced_tools:connections:christoffel_symbols |
advanced_tools:connections:levi_civita_connection [2018/04/14 13:51] theodorekorovin ↷ Links adapted because of a move operation |
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<WRAP lag>$ \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)$</WRAP> | <WRAP lag>$ \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)$</WRAP> | ||
- | ====== Levi-Civita connection ====== | + | ====== Levi-Civita Connection ====== |
//also known as Christoffel Symbols; see also [[advanced_tools:connections]] // | //also known as Christoffel Symbols; see also [[advanced_tools:connections]] // | ||
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<tabbox Intuitive> | <tabbox Intuitive> | ||
- | The Levi-Civita connection is a mathematical tool that we use to 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. |