where γ γ = det ( γ γ i j ) and G i j k l = ( γ γ i k γ γ j l + γ γ i l γ γ j k − − γ γ i j γ γ k l ) is the Wheeler–DeWitt metric. In index-free notation, the Wheeler–DeWitt metric on the space of positive definite quadratic forms g in three dimensions is