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In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham for which a conformal manifold of dimension n is realized (ambiently) as the boundary of a certain Poincaré manifold, or alternatively as the celestial sphere of a certain pseudo-Riemannian manifold. Aside from the obstruction tensor, the ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators. A related construction is the tractor bundle.

Attributes	Values
rdfs:label	Ambient construction (en)
rdfs:comment	In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham for which a conformal manifold of dimension n is realized (ambiently) as the boundary of a certain Poincaré manifold, or alternatively as the celestial sphere of a certain pseudo-Riemannian manifold. Aside from the obstruction tensor, the ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators. A related construction is the tractor bundle. (en)
dcterms:subject	Conformal geometry Tensors in general relativity
Wikipage page ID	5784666 (xsd:integer)
Wikipage revision ID	984935461 (xsd:integer)
Link from a Wikipage to another Wikipage	Pseudo-Riemannian Total space Ricci flat Lie derivative Obstruction theory Tractor bundle Pullback (differential geometry) Minkowski space Conformal geometry Order of approximation AdS/CFT correspondence GJMS operator Line bundle Conformal geometry Tensors in general relativity Celestial sphere Differential operator Dirichlet boundary condition Bach tensor Hyperbolic manifold Asymptotic Charles Fefferman Bousso's holographic bound C. Robin Graham Schouten tensor Conformal class Weyl tensor Conformal manifold Null cone dbr:Normal_conformal_connection
sameAs	Ambient construction Ambient construction Ambient construction
dbp:wikiPageUsesTemplate	dbt:Cite_arXiv
has abstract	In conformal geometry, the ambient construction refers to a construction of Charles Fefferman and Robin Graham for which a conformal manifold of dimension n is realized (ambiently) as the boundary of a certain Poincaré manifold, or alternatively as the celestial sphere of a certain pseudo-Riemannian manifold. The ambient construction is canonical in the sense that it is performed only using the conformal class of the metric: it is conformally invariant. However, the construction only works asymptotically, up to a certain order of approximation. There is, in general, an obstruction to continuing this extension past the critical order. The obstruction itself is of tensorial character, and is known as the (conformal) obstruction tensor. It is, along with the Weyl tensor, one of the two primitive invariants in conformal differential geometry. Aside from the obstruction tensor, the ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators. A related construction is the tractor bundle. (en)
prov:wasDerivedFrom	wikipedia-en:Ambient_construction?oldid=984935461&ns=0
page length (characters) of wiki page	7030 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ambient_construction
is rdfs:seeAlso of	Conformal geometry
is Link from a Wikipage to another Wikipage of	List of differential geometry topics AdS/CFT correspondence GJMS operator Ambient metric C. Robin Graham Obstruction tensor
is Wikipage redirect of	Ambient metric Obstruction tensor
is foaf:primaryTopic of	wikipedia-en:Ambient_construction

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