Nonmetricity tensor
= Nonmetricity tensor
{title2=$N_{ab c}=\nabla_cg_{ab}$}
Given a <metric tensor> and an <affine connection>, $N_{ab c}=\nabla_cg_{ab}$ measures failure of <metric compatibility>. It is symmetric in $a,b$. Some authors instead define nonmetricity as $-\nabla g$, so formulas must specify the sign. Together with the <torsion tensor>, it determines the difference from the <Levi-Civita connection>.