nLab
hyperbolic 3-space

Contents

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

  • John Parker, Chapter 5 of Hyperbolic spaces (pdf)

  • William Abikoff, The bounded model for hyperbolic 3-space and a quaternionic uniformization theorem, Mathematica Scandinavica Vol. 54, No. 1 (August 23, 1984), pp. 5-16 (jstor:24491416)

See also

Last revised on May 24, 2019 at 22:24:10. See the history of this page for a list of all contributions to it.