Hyperbolic three-manifold
= Hyperbolic three-manifold
{title2=$M=\mathbb H^3/\Gamma$}
A complete hyperbolic three-manifold is a complete <Riemannian manifold> of dimension three with constant <sectional curvature> $-1$. Its <universal cover> is <hyperbolic space> $\mathbb H^3$ and its deck group acts freely and discretely by <Riemannian isometries>. In the orientable case it is a torsion-free <Kleinian group>.