Hyperbolic manifold

From Wikipedia, the free encyclopedia

In mathematics, a hyperbolic n-manifold is a complete Riemannian n-manifold of constant sectional curvature -1.

Its thick-thin decomposition has a thin part consisting of tubular neighborhoods of closed geodesics and/or ends which are the product of a Euclidean n-1-manifold and the closed half-ray. The manifold is of finite volume if and only if its thick part is compact.

The hyperbolic structure on a finite volume hyperbolic n-manifold is unique by Mostow rigidity and so geometric invariants are in fact topological invariants.

[edit] See also

• Hyperbolic 3-manifold
• Margulis lemma
• Hyperbolic space