Riemannscher Krümmungstensor

$R_{\beta \mu \nu }^{\alpha }={\partial }_{\mu }{\mathrm{\Gamma }}_{\beta \nu }^{\alpha }-{\partial }_{\mu \nu }{\mathrm{\Gamma }}_{\beta \mu }^{\alpha }+{\mathrm{\Gamma }}_{\sigma \mu }^{\alpha }{\mathrm{\Gamma }}_{\beta \nu }^{\sigma }-{\mathrm{\Gamma }}_{\sigma \nu }^{\alpha }{\mathrm{\Gamma }}_{\beta \mu }^{\sigma }$