MathLiveChristoffel symbols of the second kind
Gives the coefficients of the Levi-Civita connection of a Riemannian or pseudo-Riemannian metric in local coordinates, computed from first derivatives of the metric tensor. Used throughout differential geometry and general relativity to write covariant derivatives and geodesic equations.
\Gamma^\rho_{\mu\nu}=\frac{1}{2}g^{\rho\sigma}\left(\partial_\mu g_{\nu\sigma}+\partial_\nu g_{\mu\sigma}-\partial_\sigma g_{\mu\nu}\right)What the symbols mean
| Christoffel symbol of the second kind (connection coefficient) | |
| inverse of the metric tensor components | |
| metric tensor components | |
| partial derivative with respect to coordinate x^\mu | |
| partial derivative with respect to coordinate x^\nu |
About this formula
- FieldMathematics
- TopicDifferential geometry
- LevelAdvanced
- Also calledChristoffel symbol, Christoffel symbols, Levi-Civita connection coefficients, Christoffel symbols formula, Christoffel symbol metric formula, connection coefficients Riemannian geometry
- SourceWikidata Q847816
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