  Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of
functions on $X.$ If $H$ has the complete Pick property then there is an
isometric map, $\Phi,$ from $X,$ with the metric induced by $H,$ into complex
hyperbolic space, $\mathbb{CH}^{n},$ with its pseudohyperbolic metric. We
investigate the relationships between the geometry of $\Phi(X)$ and the
function theory of $H$ and its multiplier algebra.
