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Subject Item
dbr:Isothermal_coordinates
rdf:type
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rdfs:label
Coordonnées isothermales Изотермическая система координат Isothermal coordinates Isotherme coördinaten
rdfs:comment
En mathématiques, et plus particulièrement en géométrie différentielle, les coordonnées isothermales d'une variété riemannienne sont des coordonnées locales où le tenseur métrique est conforme à la métrique euclidienne. Cela signifie qu'en coordonnées isothermales, la métrique riemannienne a localement la forme : où est une fonction de classe . In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form where is a positive smooth function. (If the Riemannian manifold is oriented, some authors insist that a coordinate system must agree with that orientation to be isothermal.) Изотермическая система координат поверхности евклидова пространства, малые координатные квадраты которой близки к квадратам. In de differentiële meetkunde binnen de wiskunde zijn isotherme coördinaten of conforme coördinaten lokale coördinaten op een Riemann-variëteit waarbij de metriek conform is met de Euclidische metriek. Dit betekent dat in isotherme coördinaten de Riemann-metriek lokaal de vorm heeft van: waar conformele factor, welke een gladde functie is. (Als de Riemann-variëteit georiënteerd is, beweren sommigen dat een coördinatensysteem met die oriëntatie moet overeenkomen om isotherm te zijn.)
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dbc:Differential_geometry dbc:Partial_differential_equations dbc:Coordinate_systems_in_differential_geometry
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10280254
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freebase:m.02q78h2 yago-res:Isothermal_coordinates n11:2n2Xo dbpedia-nl:Isotherme_coördinaten dbpedia-he:קואורדינטות_איזותרמיות dbpedia-ru:Изотермическая_система_координат wikidata:Q2996692 dbpedia-fr:Coordonnées_isothermales
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dbp:3loc
Addendum 1 to Chapter 9
dbp:4a
Taylor
dbp:4y
2000
dbp:1a
Korn Morrey Gauss Bers Spivak
dbp:1loc
Theorem 9.18
dbp:1y
1914 1999 1825 1958 1938
dbp:2a
Lagrange Lichtenstein Chern
dbp:2y
1916 1955 1779
dbp:3a
Spivak Ahlfors
dbp:3p
90
dbp:3y
2006 1999
dbp:id
p/i052890
dbp:title
Isothermal coordinates
dbp:4loc
Proposition 3.9.3
dbo:abstract
In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form where is a positive smooth function. (If the Riemannian manifold is oriented, some authors insist that a coordinate system must agree with that orientation to be isothermal.) Isothermal coordinates on surfaces were first introduced by Gauss. Korn and Lichtenstein proved that isothermal coordinates exist around any point on a two dimensional Riemannian manifold. By contrast, most higher-dimensional manifolds do not admit isothermal coordinates anywhere; that is, they are not usually locally conformally flat. In dimension 3, a Riemannian metric is locally conformally flat if and only if its Cotton tensor vanishes. In dimensions > 3, a metric is locally conformally flat if and only if its Weyl tensor vanishes. En mathématiques, et plus particulièrement en géométrie différentielle, les coordonnées isothermales d'une variété riemannienne sont des coordonnées locales où le tenseur métrique est conforme à la métrique euclidienne. Cela signifie qu'en coordonnées isothermales, la métrique riemannienne a localement la forme : où est une fonction de classe . Les coordonnées isothermales sur les surfaces ont d'abord été introduites par Gauss. Korn et Lichtenstein ont par la suite prouvé que les coordonnées isothermales existent autour de tout point d'une variété riemannienne de dimension 2. Sur des variétés riemanniennes de dimension supérieure, une condition nécessaire et suffisante pour leur existence locale est l'annulation du tenseur de Weyl et du tenseur de Cotton-York. Изотермическая система координат поверхности евклидова пространства, малые координатные квадраты которой близки к квадратам. In de differentiële meetkunde binnen de wiskunde zijn isotherme coördinaten of conforme coördinaten lokale coördinaten op een Riemann-variëteit waarbij de metriek conform is met de Euclidische metriek. Dit betekent dat in isotherme coördinaten de Riemann-metriek lokaal de vorm heeft van: waar conformele factor, welke een gladde functie is. (Als de Riemann-variëteit georiënteerd is, beweren sommigen dat een coördinatensysteem met die oriëntatie moet overeenkomen om isotherm te zijn.)
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15549
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