About: Weyl–Schouten theorem

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In the mathematical field of differential geometry, the existence of isothermal coordinates for a (pseudo-)Riemannian metric is often of interest. In the case of a metric on a two-dimensional space, the existence of isothermal coordinates is unconditional. For higher-dimensional spaces, the Weyl–Schouten theorem (named after Hermann Weyl and Jan Arnoldus Schouten) characterizes the existence of isothermal coordinates by certain equations to be satisfied by the Riemann curvature tensor of the metric.

Attributes	Values
rdf:type	yago:WikicatTheoremsInRiemannianGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Weyl–Schouten theorem (en)
rdfs:comment	In the mathematical field of differential geometry, the existence of isothermal coordinates for a (pseudo-)Riemannian metric is often of interest. In the case of a metric on a two-dimensional space, the existence of isothermal coordinates is unconditional. For higher-dimensional spaces, the Weyl–Schouten theorem (named after Hermann Weyl and Jan Arnoldus Schouten) characterizes the existence of isothermal coordinates by certain equations to be satisfied by the Riemann curvature tensor of the metric. (en)
dcterms:subject	Theorems in Riemannian geometry
Wikipage page ID	6129957 (xsd:integer)
Wikipage revision ID	1106356123 (xsd:integer)
Link from a Wikipage to another Wikipage	Theorems in Riemannian geometry Princeton University Press Scalar curvature Bianchi identities Ricci curvature Frobenius theorem (differential topology) Closed and exact differential forms Springer Publishing Graduate Texts in Mathematics Riemann curvature tensor Pseudo-Riemannian manifold Riemannian metric Hermann Weyl Isothermal coordinates Jan Arnoldus Schouten Codazzi tensor Differential geometry Yamabe problem Schouten tensor Weyl tensor Poincaré lemma Springer-Verlag Ricci tensor Conformally flat
sameAs	Weyl–Schouten theorem Weyl–Schouten theorem Weyl–Schouten theorem
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_book dbt:Math dbt:Mvar dbt:Reflist dbt:Sfnm dbt:Short_description
1a	Aubin (en)
1loc	Definition 4.23 (en) Theorem 4.24 (en)
1p	118 (xsd:integer)
1y	1998 (xsd:integer)
2a	Eisenhart (en)
2p	91 (xsd:integer)
2y	1926 (xsd:integer)
2loc	Section 28 (en)
has abstract	In the mathematical field of differential geometry, the existence of isothermal coordinates for a (pseudo-)Riemannian metric is often of interest. In the case of a metric on a two-dimensional space, the existence of isothermal coordinates is unconditional. For higher-dimensional spaces, the Weyl–Schouten theorem (named after Hermann Weyl and Jan Arnoldus Schouten) characterizes the existence of isothermal coordinates by certain equations to be satisfied by the Riemann curvature tensor of the metric. Existence of isothermal coordinates is also called conformal flatness, although some authors refer to it instead as local conformal flatness; for those authors, conformal flatness refers to a more restrictive condition. (en)
gold:hypernym	Tensor
prov:wasDerivedFrom	wikipedia-en:Weyl–Schouten_theorem?oldid=1106356123&ns=0
page length (characters) of wiki page	7019 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weyl–Schouten_theorem
is Link from a Wikipage to another Wikipage of	List of differential geometry topics Conformally flat manifold Hermann Weyl Jan Arnoldus Schouten Codazzi tensor Schouten Schouten tensor List of things named after Hermann Weyl Weyl-Schouten theorem
is Wikipage redirect of	Weyl-Schouten theorem
is Wikipage disambiguates of	Schouten
is foaf:primaryTopic of	wikipedia-en:Weyl–Schouten_theorem

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