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geometry > non-Euclidean geometry > hyperbolic geometry > hyperbolic space
... > topology > algebraic topology > manifold > differentiable manifold > Lie group > homogeneous space > hyperbolic space
... > geometry > topological space > manifold > differentiable manifold > Lie group > homogeneous space > hyperbolic space
... > geometry > differential geometry > differentiable manifold > Lie group > homogeneous space > hyperbolic space
... > topology > differential topology > differentiable manifold > Lie group > homogeneous space > hyperbolic space
... > algebra > group theory > topological group > Lie group > homogeneous space > hyperbolic space
algebra > abstract algebra > algebraic structure > homogeneous space > hyperbolic space

Preferred term

hyperbolic space  

Definition(s)

  • In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space. There are many ways to construct it as an open subset of with an explicitly written Riemannian metric; such constructions are referred to as models. Hyperbolic 2-space, H2, which was the first instance studied, is also called the hyperbolic plane.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperbolic_space)

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Related concept(s)

Synonym(s)

  • Bolyai-Lobachevsky space
  • Lobachevsky space

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URI

http://data.loterre.fr/ark:/67375/PSR-RSS68597-V

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