About: Cartan's equivalence method

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In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism such that ? The equivalence method is an essentially algorithmic procedure for determining when two geometric structures are identical. For Cartan, the primary geometrical information was expressed in a coframe or collection of coframes on a differentiable manifold. See method of moving frames.

Attributes	Values
rdfs:label	Cartan's equivalence method (en)
rdfs:comment	In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism such that ? The equivalence method is an essentially algorithmic procedure for determining when two geometric structures are identical. For Cartan, the primary geometrical information was expressed in a coframe or collection of coframes on a differentiable manifold. See method of moving frames. (en)
dcterms:subject	Diffeomorphisms Differential geometry
Wikipage page ID	1841654 (xsd:integer)
Wikipage revision ID	862708484 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Algorithm Diffeomorphisms Riemann Lie group Trivial group Differential geometry Mathematics Orthonormal Pullback (differential geometry) Elwin Bruno Christoffel Frobenius theorem (differential topology) Gaussian elimination Complex manifold Élie Cartan G-structure Jet group Exterior derivative Cartan-Kähler theorem Diffeomorphism Riemannian manifold Lagrangian mechanics Coframe Differentiable manifold Differential geometry D. C. Spencer Method of moving frames Ordinary differential equation Cartan–Karlhede algorithm Shiing-Shen Chern Real analytic CR structure dbr:Cartan's_test dbr:Projective_structure dbr:Prolongation_of_G-structures
sameAs	Cartan's equivalence method Cartan's equivalence method Cartan's equivalence method
dbp:wikiPageUsesTemplate	dbt:Cite_book
has abstract	In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism such that ? Although the answer to this particular question was known in dimension 2 to Gauss and in higher dimensions to Christoffel and perhaps Riemann as well, Élie Cartan and his intellectual heirs developed a technique for answering similar questions for radically different geometric structures. (For example see the Cartan–Karlhede algorithm.) Cartan successfully applied his equivalence method to many such structures, including , CR structures, and complex structures, as well as ostensibly non-geometrical structures such as the equivalence of Lagrangians and ordinary differential equations. (His techniques were later developed more fully by many others, such as D. C. Spencer and Shiing-Shen Chern.) The equivalence method is an essentially algorithmic procedure for determining when two geometric structures are identical. For Cartan, the primary geometrical information was expressed in a coframe or collection of coframes on a differentiable manifold. See method of moving frames. (en)
prov:wasDerivedFrom	wikipedia-en:Cartan's_equivalence_method?oldid=862708484&ns=0
page length (characters) of wiki page	8399 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Cartan's_equivalence_method
is Link from a Wikipage to another Wikipage of	List of differential geometry topics Paulette Libermann Peter J. Olver Connection (mathematics) Contorsion tensor G-structure on a manifold Differential ideal Differential invariant Moving frame Jet bundle Torsion tensor List of things named after Élie Cartan Robert Brown Gardner Cartan equivalence method Theory of equivalence
is Wikipage redirect of	Cartan equivalence method Theory of equivalence
is foaf:primaryTopic of	wikipedia-en:Cartan's_equivalence_method

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