the pullback of the Minkowski metric under inclusion, is a Riemannian metric. With this metric is a Riemannian manifold. It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space. It is a space of constant negative curvature . The in the upper index refers to an enumeration of the different model spaces of hyperbolic geometry, and the for its dimension. A corresponds to the Poincaré disk model, while corresponds to the Poincaré half-space model of dimension .