Christoffel symbols

Summary

The Christoffel symbols $\Gamma^k_{ij}$ are the components of an affine connection in a coordinate chart. They record how the covariant derivative of one coordinate vector field along another fails to vanish. For the Levi-Civita connection of a Riemannian metric they are given by an explicit formula in the first derivatives of the metric. They appear in the geodesic equation and in coordinate formulas for curvature.