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- Poincaré_metric abstract "In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces.There are three equivalent representations commonly used in two-dimensional hyperbolic geometry. One is the Poincaré half-plane model, defining a model of hyperbolic space on the upper half-plane. The Poincaré disk model defines a model for hyperbolic space on the unit disk. The disk and the upper half plane are related by a conformal map, and isometries are given by Möbius transformations. A third representation is on the punctured disk, where relations for q-analogues are sometimes expressed. These various forms are reviewed below.".
- Poincaré_metric wikiPageID "1487868".
- Poincaré_metric wikiPageLength "8948".
- Poincaré_metric wikiPageOutDegree "56".
- Poincaré_metric wikiPageRevisionID "673674026".
- Poincaré_metric wikiPageWikiLink Annulus_(mathematics).
- Poincaré_metric wikiPageWikiLink Category:Conformal_geometry.
- Poincaré_metric wikiPageWikiLink Category:Hyperbolic_geometry.
- Poincaré_metric wikiPageWikiLink Category:Riemann_surfaces.
- Poincaré_metric wikiPageWikiLink Category:Riemannian_geometry.
- Poincaré_metric wikiPageWikiLink Codomain.
- Poincaré_metric wikiPageWikiLink Conformal_map.
- Poincaré_metric wikiPageWikiLink Contraction_mapping.
- Poincaré_metric wikiPageWikiLink Cross-ratio.
- Poincaré_metric wikiPageWikiLink Curvature.
- Poincaré_metric wikiPageWikiLink Exterior_algebra.
- Poincaré_metric wikiPageWikiLink Exterior_product.
- Poincaré_metric wikiPageWikiLink Fuchsian_group.
- Poincaré_metric wikiPageWikiLink Fuchsian_model.
- Poincaré_metric wikiPageWikiLink Geodesic.
- Poincaré_metric wikiPageWikiLink Geodesics.
- Poincaré_metric wikiPageWikiLink Geometry.
- Poincaré_metric wikiPageWikiLink Half-period_ratio.
- Poincaré_metric wikiPageWikiLink Henri_Poincaré.
- Poincaré_metric wikiPageWikiLink Hyperbolic_geometry.
- Poincaré_metric wikiPageWikiLink Isometry.
- Poincaré_metric wikiPageWikiLink Kleinian_group.
- Poincaré_metric wikiPageWikiLink Kleinian_model.
- Poincaré_metric wikiPageWikiLink Laplace_operator.
- Poincaré_metric wikiPageWikiLink Laplace–Beltrami_operator.
- Poincaré_metric wikiPageWikiLink Mathematics.
- Poincaré_metric wikiPageWikiLink Metric_tensor.
- Poincaré_metric wikiPageWikiLink Möbius_transformation.
- Poincaré_metric wikiPageWikiLink Nome_(mathematics).
- Poincaré_metric wikiPageWikiLink Poincaré_disk_model.
- Poincaré_metric wikiPageWikiLink Poincaré_half-plane_model.
- Poincaré_metric wikiPageWikiLink Prime_geodesic.
- Poincaré_metric wikiPageWikiLink Punctured_disk.
- Poincaré_metric wikiPageWikiLink Q-analog.
- Poincaré_metric wikiPageWikiLink Ricci_scalar_curvature.
- Poincaré_metric wikiPageWikiLink Riemann_sphere.
- Poincaré_metric wikiPageWikiLink Riemann_surface.
- Poincaré_metric wikiPageWikiLink SL2(R).
- Poincaré_metric wikiPageWikiLink Scalar_curvature.
- Poincaré_metric wikiPageWikiLink Schwarz_lemma.
- Poincaré_metric wikiPageWikiLink Schwarz–Ahlfors–Pick_theorem.
- Poincaré_metric wikiPageWikiLink Svetlana_Katok.
- Poincaré_metric wikiPageWikiLink Unit_disc.
- Poincaré_metric wikiPageWikiLink Unit_disk.
- Poincaré_metric wikiPageWikiLink Upper_half-plane.
- Poincaré_metric wikiPageWikiLink Volume_element.
- Poincaré_metric wikiPageWikiLink Volume_form.
- Poincaré_metric wikiPageWikiLink File:J-inv-modulus.jpeg.
- Poincaré_metric wikiPageWikiLink File:J-inv-poincare.jpeg.
- Poincaré_metric wikiPageWikiLinkText "Poincaré disk".
- Poincaré_metric wikiPageWikiLinkText "Poincaré metric".
- Poincaré_metric wikiPageWikiLinkText "Poincaré".
- Poincaré_metric wikiPageWikiLinkText "hyperbolic disks".
- Poincaré_metric hasPhotoCollection Poincaré_metric.
- Poincaré_metric subject Category:Conformal_geometry.
- Poincaré_metric subject Category:Hyperbolic_geometry.
- Poincaré_metric subject Category:Riemann_surfaces.
- Poincaré_metric subject Category:Riemannian_geometry.
- Poincaré_metric comment "In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces.There are three equivalent representations commonly used in two-dimensional hyperbolic geometry. One is the Poincaré half-plane model, defining a model of hyperbolic space on the upper half-plane.".
- Poincaré_metric label "Poincaré metric".
- Poincaré_metric sameAs Métrique_de_Poincaré.
- Poincaré_metric sameAs ポアンカレ計量.
- Poincaré_metric sameAs m.0559mh.
- Poincaré_metric sameAs Метрика_Пуанкаре.
- Poincaré_metric sameAs Q377798.
- Poincaré_metric sameAs Q377798.
- Poincaré_metric sameAs 庞加莱度量.
- Poincaré_metric wasDerivedFrom Poincaré_metric?oldid=673674026.
- Poincaré_metric isPrimaryTopicOf Poincaré_metric.