Hyperbolic manifold

Hyperbolic manifold

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.

For n>2 the hyperbolic structure on a "finite volume" hyperbolic "n"-manifold is unique by Mostow rigidity and so geometric invariants are in fact topological invariants.

ee also

* Hyperbolic 3-manifold
* Margulis lemma
* Hyperbolic space


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