Generalized uncertainty principle or curved momentum space?

The concept of minimum length, widely accepted as a low-energy effect quantum gravity, manifests itself in mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at heart similar applications such doubly special relativity. We introduce duality between theories yielding principles and nontrivial space. In particular, we find canonically conjugate variables which map former into latter. that vein, explicitly derive vielbein corresponding to generic principle $d$ dimensions. Assuming predominantly used quadratic form modification, curvature tensor space proportional noncommutativity coordinates modified Heisenberg algebra. Yet, metric non-Euclidean even flat case commutative because resulting basis noncanonical. These insides are constrain deviation from canonical basis.