Definition:Christoffel Symbol

Definition
Let $\struct {M, g}$ be a Riemannian or pseudo-Riemannian manifold.

Let $\nabla$ be the Levi-Civita connection of $\struct {M, g}$.

Suppose $\Gamma^k_{ij}$ are the connection coefficients of $\nabla$.

Then $\Gamma^k_{ij}$ are called the Christoffel symbols.