English

The ambient metric

Differential Geometry 2008-10-22 v2

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.

Keywords

Cite

@article{arxiv.0710.0919,
  title  = {The ambient metric},
  author = {Charles Fefferman and C. Robin Graham},
  journal= {arXiv preprint arXiv:0710.0919},
  year   = {2008}
}

Comments

v2: 100 pages, introduction rewritten, minor editorial changes elsewhere

R2 v1 2026-06-21T09:26:28.761Z