Riemann R^ρ_{σμν}=∂_μΓ^ρ_{νσ}−∂_νΓ^ρ_{μσ}+ΓΓ−ΓΓ; (4,0) symmetries

Riemann curvature tensor R^ρ_{σμν} of a Levi-Civita connection measures the non-commutativity of second covariant derivatives: [∇_μ, ∇_ν] V^ρ = R^ρ_{σμν} V^σ. Coordinate expression: R^ρ_{σμν} = ∂_μ Γ^ρ_{νσ} − ∂_ν Γ^ρ_{μσ} + Γ^ρ_{μλ}…