nLab
hyperbolic 3-space

Contents

Idea

Hyperbolic 3-space 3\mathbb{H}^3 is the simply connected geodesically complete hyperbolic 3-manifold.

Every hyperbolic 3-manifold is isometric to the quotient space 3/Γ\mathbb{H}^3/\Gamma of hyperbolic 3-space by the action of a torsion-free discrete group acting via isometries.

References

See also