The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic equation. There are two closely related kinds of Christoffel symbols, the first kind Γ_(i, j, k), and the second kind Γ_(i, j)^k. Christoffel symbols of the second kind are also known as affine connections or connection coefficients .

Christoffel symbol of the first kind | Christoffel symbol of the second kind | geodesic | Levi-Civita connection | Riemannian geometry