More generally, ∇ ∇ ⋅ ⋅ S = [ ∂ ∂ S i j ∂ ∂ q k − − Γ Γ k i l S l j − − Γ Γ k j l S i l ] g i k b j = [ ∂ ∂ S i j ∂ ∂ q i + Γ Γ i l i S l j + Γ Γ i l j S i l ] b j = [ ∂ ∂ S j i ∂ ∂ q i + Γ Γ i l i S j l − − Γ Γ i j l S l i ] b j = [ ∂ ∂ S i j ∂ ∂ q k − − Γ Γ i k l S l j + Γ Γ k l j S i l ] g i k b j