Hyperboloid model
= Hyperboloid model
{wiki}
The hyperboloid model of the curvature-minus-one hyperbolic plane is
$$
\{x\in\mathbb R^3:-x_0^2+x_1^2+x_2^2=-1, x_0>0\}.
$$
Its metric is the restriction of the Minkowski bilinear form to tangent planes, and its geodesics are intersections with two-dimensional linear subspaces through the origin.