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035   $a(DE-B1597)9781400840588
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100   $a20110714d2012      uy         0
101 0 $aeng
135   $aurnn#---|u||u
181   $ctxt
182   $cc
183   $acr
200 14$aThe ambient metric /$fCharles Fefferman, C. Robin Graham
205   $aCourse Book
210   $aPrinceton $cPrinceton University Press$d2012
215   $a1 online resource (124 p.)
225 1 $aAnnals of mathematics studies ;$vno. 178
300   $aDescription based upon print version of record.
311   $a0-691-15313-2 
311   $a0-691-15314-0 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tChapter One. Introduction --$tChapter Two. Ambient Metrics --$tChapter Three. Formal Theory --$tChapter Four. Poincaré Metrics --$tChapter Five. Self-dual Poincaré Metrics --$tChapter Six. Conformal Curvature Tensors --$tChapter Seven. Conformally Flat and Conformally Einstein Spaces --$tChapter Eight. Jet Isomorphism --$tChapter Nine. Scalar Invariants --$tBibliography --$tIndex
330   $aThis book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
410  0$aAnnals of mathematics studies ;$vno. 178.
606   $aConformal geometry
606   $aConformal invariants
610   $aEistein metric.
610   $aFuchsian problems.
610   $aLorentz metric.
610   $aPoincar metric.
610   $aPoincar metrics.
610   $aRicci curvature.
610   $aRiemannian geometry.
610   $aRiemannian metrics.
610   $aTaylor expansion.
610   $aWeyl invariants.
610   $aambient curvature.
610   $aambient metric forms.
610   $aambient metric.
610   $aconformal curvature tensors.
610   $aconformal geometry.
610   $aconformal infinity.
610   $aconformal invariants.
610   $aconformal manifold.
610   $aflat manifolds.
610   $ageodesic normal coordinates.
610   $ainfinite-order formal theory.
610   $ajet isomorphism theorem.
610   $amanifold.
610   $an+2 dimensions.
610   $aparabolic invariant theory.
610   $apower series.
610   $apseudo-Riemannian metric.
610   $ascalar invariants.
610   $aself-dual Einstein metric.
610   $atheorem.
615  0$aConformal geometry.
615  0$aConformal invariants.
676   $a516.3/7
686   $aMAT012020$2bisacsh
700   $aFefferman$b Charles$f1949-$0476528
701   $aGraham$b C. Robin$f1954-$01650516
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910819324903321
996   $aThe ambient metric$93999934
997   $aUNINA