Levi-Civita Γ^k_{ij} = ½ g^{kl}(∂_i g_{jl}+∂_j g_{il}−∂_l g_{ij})

Christoffel symbols of the second kind Γ^k_{ij} are the connection coefficients of the unique torsion-free metric-compatible ('Levi-Civita', 1917) connection ∇ on a (pseudo-)Riemannian manifold. Fundamental theorem of Riemannian geometry:…