Christoffel Symbol

$${\Gamma }_{\beta \gamma }^{\delta }=\frac{1}{2}{g}^{\alpha \delta }\left(\frac{d{g}_{\alpha \beta }}{d{x}^{\gamma }}+\frac{d{g}_{\alpha \gamma }}{d{x}^{\beta }}-\frac{d{g}_{\beta \gamma }}{d{x}^{\alpha }}\right)$$

See also

Spacetime Metric Ricci Tensor