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(1) [itex]G_{\alpha\beta}[/itex]=[itex]R_{\alpha\beta}[/itex]-[itex]\frac{1}{2}[/itex][itex]g_{\alpha\beta}[/itex]R

(2) [itex]G_{\alpha\beta}[/itex]+[itex]\Lambda[/itex][itex]g_{\alpha\beta}[/itex]=0

(3) [itex]R_{\alpha\beta\gamma\delta}[/itex] = [itex]g_{\alpha\gamma}[/itex][itex]R_{\beta\delta}[/itex]+[itex]g_{\beta\delta}[/itex][itex]R_{\alpha\gamma}[/itex]-[itex]g_{\alpha\delta}[/itex][itex]R_{\beta\gamma}[/itex]-[itex]g_{\beta\gamma}[/itex][itex]R_{\alpha\delta}[/itex]-[itex]\frac{R}{2}[/itex]([itex]g_{\alpha\gamma}[/itex][itex]g_{\beta\delta}[/itex]-[itex]g_{\alpha\delta}[/itex][itex]g_{\beta\gamma}[/itex])

= [itex]\Lambda[/itex]([itex]g_{\alpha\gamma}[/itex][itex]g_{\beta\delta}[/itex]-[itex]g_{\alpha\delta}[/itex][itex]g_{\beta\gamma}[/itex])