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