(48)
∂H/∂_g_^{μν} = -Γ_{μβ}^{α} Γ_{να}^{β}
∂H/∂_g__{σ}^{μν} = Γ_{μν}^{σ}
If we now carry out the variations in (47a), we obtain the system of
equations
(47b) ∂/∂_x__{α} ( ∂H/∂_g__{α}^{μν} ) - ∂H/∂_g_^{μν} = 0,
which, owing to the relations (48), coincide with (47), as was required
to be proved.