About: Conformal geometry

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In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry.

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rdf:type	Thing book
rdfs:label	Conformal geometry (en) Konformní geometrie (cs) Geometria conforme (it) Hoekgetrouwe meetkunde (nl) Geometria konforemna (pl) Geometria conforme (pt) Конформна геометрія (uk)
rdfs:comment	Konformní geometrie je geometrický obor, který studuje transformace prostorů, které zachovávají úhly. Transformace, která zachovává úhly vektorů se nazývá konformní. V reálné dimenzi dva konformní geometrie studuje geometrii . Obecněji jsou předmětem studia konformní geometrie tzv. , což jsou hladké variety na kterých je definována třída metrik, kterése všechny liší jenom o násobek nezáporné skalární funkce. Díky tomu jsme na varietě schopny měřit úhly tečných vektorů. Speciálně každá Riemannova varieta určuje příslušnou konformní strukturu. (cs) In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry. (en) In de wiskunde is de hoekgetrouwe meetkunde de studie van de verzameling van hoek-conserverende transformaties op een Riemann-variëteit of pseudo-Riemann-variëteit. De hoekgetrouwe meetkunde in twee (reële) dimensies in het bijzonder is de meetkunde van Riemann-oppervlakken. (nl) In matematica, la geometria conforme è la geometria delle trasformazioni del piano che lasciano invariati gli angoli. In due dimensioni reali, la geometria conforme è precisamente la geometria della superficie di Riemann. Nel caso di più dimensioni si può riferire allo studio delle funzioni di trasformazione conforme di spazi piatti (come lo spazio euclideo o le sfere), o, più comunemente, allo studio delle varietà riemanniane o pseudo-riemanniane dotate di metriche in relazione tra loro mediante una trasformazione conforme (varietà conformi). Lo studio delle varietà piatte a volte è chiamata anche geometria di Möbius, ed è una tipologia di geometria di Klein. Lo studio della geometria conforme ha numerose implicazioni nella fisica teorica e nella cosmologia. (it) Geometria konforemna – dział badający odwzorowania równokątne (zachowujące kąt, konforemne) określone na rozmaitościach riemmanowskich lub rozmaitościach pseudoriemannowskich. W szczególności geometria konforemna w dwóch (rzeczywistych) wymiarach jest geometrią płaszczyzn riemannowskich. (pl) Em matemática, geometria conforme é o estudo do conjunto de transformações de um ângulo-conforme em um espaço. Em duas dimensões reais, a geometria conforme é precisamente a geometria das superfícies de Riemann. Em mais de duas dimensões, geometria conforme pode se referir tanto ao estudo das transformações dos ângulos no espaço (como espaços euclidianos ou esferas), ou, mais comumente, para o estudo das variedades conformes que estão dentro das variedades de Riemann com uma classe de métricas definidas em escala. Estudo dessas estruturas é às vezes chamado de geometria Möbius, e é um tipo de . (pt) В математиці, конформна геометрія — це її розділ, що вивчає такі перетворення простору, що зберігають значення кутів у зображенні цього простору (конформні перетворення). В дійсному двомірному просторі конформна геометрія описує саме геометрію Ріманових поверхонь. У просторах вищих розмірностей, конформною геометрією називають або конформні перетворення того, що називають плоскими просторами (такі як простори Евкліда або ж сфери), або вивчення конформних многовидів які є Рімановими або псевдо-Рімановими многовидами з метриками означеними з точністю до масштабу. Вивчення плоских структур деколи називають геометрією Мьобіуса, це різновид . (uk)
rdfs:seeAlso	Ambient construction Virasoro algebra
foaf:depiction
dcterms:subject	Differential geometry Conformal geometry
Wikipage page ID	295907 (xsd:integer)
Wikipage revision ID	1086882705 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartan–Dieudonné theorem Projective space Quadric Multiplicative group Borel subalgebra Holomorphic function Homogeneous space Curvature form Inversive geometry Lie group Light cone Differential geometry Compact space Complex plane Conformal geometric algebra Mathematics Geodesic Geometry Minkowski plane Minkowski space Möbius transformation N-sphere Conformal connection Conformal field theory Conformal geometry Conformal gravity Conformal group Conformal map Conformally flat manifold Coordinate system Erlangen program Levi-Civita connection Lie algebra Liouville's theorem (conformal mappings) Lorentz transformation Smooth function Stereographic projection Compactification (mathematics) Symmetry Line bundle Local diffeomorphism Conformal geometry Euclidean space Celestial sphere Riemann curvature tensor Quadratic form Projective linear group Pseudo-Riemannian manifold Riemannian geometry Riemannian manifold Riemannian metric Isometry Cotton tensor Riemann sphere Riemann surfaces Abelian group Diffeomorphism group Metric tensor Cartan connection Cartan decomposition Klein geometry Hypersphere Mutatis mutandis Metric signature Up to Conformal Killing equation Möbius plane Witt algebra Weyl tensor Tangent vector Two-dimensional conformal field theory Universal cover Cauchy–Riemann equation Christoffel symbol Conformal mapping Möbius geometry

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