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The Ambient Metric (AM-178) by C. Graham, Charles Fefferman

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Chapter Eight

 

Jet Isomorphism

A fundamental result in Riemannian geometry is the jet isomorphism theorem which asserts that at the origin in geodesic normal coordinates, the full Taylor expansion of the metric may be recovered from the iterated covariant derivatives of curvature. As a consequence, one deduces that any local invariant of Riemannian metrics has a universal expression in terms of the curvature tensor and its covariant derivatives. Geodesic normal coordinates are determined up to the orthogonal group, so problems involving local invariants are reduced to purely algebraic questions concerning invariants of the orthogonal group on tensors.

Our goal in this chapter is to prove an analogous jet isomorphism theorem for conformal ...

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