Hyperbolic surface
= Hyperbolic surface
{title2=$K_{\rm Gaussian}=-1$}
A surface with a complete <Riemannian metric> of constant <Gaussian curvature> $-1$. Its local model is the <Poincare half-plane model>; the orientable case is a quotient by a free <properly discontinuous group action> of orientation-preserving isometries.