Cayley-Klein-Hilbert Metric

The Metric of Felix Klein's model for Hyperbolic Geometry,

$$\begin{eqnarray*} g_{11} &=& {a^2(1-{x_2}^2)\over (1-{x_1}^2-{x_2}^2)^2}\\ g_... ...)^2}\\ g_{22} &=& {a^2(1-{x_1}^2)\over (1-{x_1}^2-{x_2}^2)^2}. \end{eqnarray*}$$

See also Hyperbolic Geometry