In order to exhibit the metric, it is necessary to pull it back via a suitable parametrization. A parametrization of a submanifold S of M is a map U ⊂ R → M whose range is an open subset of S. If S has the same dimension as M, a parametrization is just the inverse of a coordinate map φ : M → U ⊂ R. The parametrization to be used is the inverse of hyperbolic stereographic projection. This is illustrated in the figure to the right for n = 2. It is instructive to compare to stereographic projection for spheres.