R α β μ ν = ∂ μ Γ β ν α − ∂ ν Γ β μ α + Γ σ μ α Γ β ν σ − Γ σ ν α Γ β μ σ {\displaystyle {R^{\color {Violet}\alpha }}_{{\color {WildStrawberry}\beta }{\color {Orange}\mu }{\color {Red}\nu }}={\partial _{\color {Orange}\mu }}\Gamma _{{\color {WildStrawberry}\beta }{\color {Red}\nu }}^{\color {Violet}\alpha }-{\partial _{\color {Red}\nu }}\Gamma _{{\color {WildStrawberry}\beta }{\color {Orange}\mu }}^{\color {Violet}\alpha }+\Gamma _{\sigma {\color {Orange}\mu }}^{\color {Violet}\alpha }\Gamma _{{\color {WildStrawberry}\beta }{\color {Red}\nu }}^{\sigma }-\Gamma _{\sigma {\color {Red}\nu }}^{\color {Violet}\alpha }\Gamma _{{\color {WildStrawberry}\beta }{\color {Orange}\mu }}^{\sigma }}