Loterre: Mathematics: hyperbolic manifold

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topology > differential topology > differentiable manifold > Riemannian manifold > hyperbolic manifold

geometry > differential geometry > Riemannian geometry > Riemannian manifold > hyperbolic manifold

geometry > non-Euclidean geometry > hyperbolic geometry > hyperbolic manifold

hyperbolic manifold

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in dimensions 2 and 3, where they are called hyperbolic surfaces and hyperbolic 3-manifolds, respectively. In these dimensions, they are important because most manifolds can be made into a hyperbolic manifold by a homeomorphism. This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperbolic_manifold)

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