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Concept information

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

Preferred term

hyperbolic motion  

Definition

  • In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous group. This group is said to characterize the hyperbolic space. Such an approach to geometry was cultivated by Felix Klein in his Erlangen program. The idea of reducing geometry to its characteristic group was developed particularly by Mario Pieri in his reduction of the primitive notions of geometry to merely point and motion.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperbolic_motion)

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http://data.loterre.fr/ark:/67375/PSR-V2DP2SGJ-N

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