The most commonly used identity involving the curl of a tensor field, T , is ∇ ∇ × × ( ∇ ∇ T ) = 0 This identity holds for tensor fields of all orders. For the important case of a second-order tensor, S , this identity implies that ∇ ∇ × × ( ∇ ∇ S ) = 0 ⟹ ⟹ S m i , j − − S m j , i = 0