Disformation tensor ($W_{abc}=\frac{1}{2}(N_{abc}-N_{bca}-N_{cab})$)

With derivative-last connection coefficients and $N_{abc}={\nabla }_c{g}_{ab}$, the displayed tensor is the symmetric-in-$a,b$ correction associated with the nonmetricity tensor. Raising its final slot gives the correction to connection coefficients. It vanishes for metric compatibility. Reversing the sign used to define nonmetricity reverses this formula.