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Mathematics > Differential Geometry

arXiv:0710.0919 (math)
[Submitted on 4 Oct 2007 (v1), last revised 22 Oct 2008 (this version, v2)]

Title:The ambient metric

Authors:Charles Fefferman, C. Robin Graham
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Abstract: This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is established. Definitions and properties of conformal curvature tensors defined by ambient metrics together with formulation and proof of a jet isomorphism theorem with application to the characterization of scalar conformal invariants are given.
Comments: v2: 100 pages, introduction rewritten, minor editorial changes elsewhere
Subjects: Differential Geometry (math.DG)
MSC classes: 53B20
Cite as: arXiv:0710.0919 [math.DG]
  (or arXiv:0710.0919v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.0919

Submission history

From: C. Robin Graham [view email]
[v1] Thu, 4 Oct 2007 03:15:07 UTC (88 KB)
[v2] Wed, 22 Oct 2008 01:38:58 UTC (92 KB)
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