About: Isothermal coordinates

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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.)

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rdfs:label	Isothermal coordinates (en) Coordonnées isothermales (fr) Isotherme coördinaten (nl) Изотермическая система координат (ru)
rdfs:comment	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.) (nl) Изотермическая система координат поверхности евклидова пространства, малые координатные квадраты которой близки к квадратам. (ru) 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.) (en) 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 . (fr)
dct:subject	Differential geometry Coordinate systems in differential geometry Partial differential equations
Wikipage page ID	10280254 (xsd:integer)
Wikipage revision ID	1108570572 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Carl Friedrich Gauss Beltrami equation Mitsuhiro Shishikura Coordinate chart Euclidean metric Hodge star operator Holomorphic function Richard M. Pollack Riemann surface Inverse function theorem Differential geometry Courant Institute of Mathematical Sciences Analytic function Mathematics Elliptic partial differential equation Gaussian curvature Conformal geometry Conformal map Antoni Zygmund Leon Lichtenstein Liouville's equation Lipman Bers Smooth function Complex manifold Proceedings of the American Mathematical Society Mathematical Surveys and Monographs Measurable Riemann mapping theorem Adrien Douady Alberto Calderón American Mathematical Society Partial differential equations Cauchy–Kowalevski theorem Coordinate systems in differential geometry Dover Publications, Inc. Riemannian manifold Riemannian metric Harmonic function Irwin Kra Cotton tensor Arthur Korn Partial differential equations John H. Hubbard Lars Ahlfors Differential geometry Springer Science+Business Media McGraw-Hill Book Co. Hölder continuous Metric tensor New York University Complex derivative Weyl tensor Poincaré lemma Joseph Lagrange Transactions of the American Mathematical Society Transition map Shiing-shen Chern Springer-Verlag Charles Morrey Quasiconformal map Singular integral operator Clifford Earle Locally conformally flat Surfaces of revolution
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=BWAWAQAAIAAJ https://books.google.com/books%3Fid=U1ZFAAAAcAAJ https://books.google.com/books%3Fid=pgizxQ8X-WUC http://www.numdam.org/item%3Fid=ASENS_1981_4_14_3_249_0 https://archive.org/details/sourcebookinmath00smit%7Cpages=463%E2%80%93475%7Cencyclopedia=A http://sites.mathdoc.fr/cgi-bin/oeitem%3Fid=OE_LAGRANGE__4_637_0%7Clocation=Paris%7Cpublisher=Gauthier-Villars%7Clanguage=French%7Ceditor-link1=Joseph
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