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The Ambient Metric (AM-178)$
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Charles Fefferman and C. Robin Graham

Print publication date: 2011

Print ISBN-13: 9780691153131

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153131.001.0001

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Scalar Invariants

Scalar Invariants

(p.97) Chapter Nine Scalar Invariants
The Ambient Metric (AM-178)

Charles Fefferman

C. Robin Graham

Princeton University Press

This chapter shows how to derive a characterization of scalar invariants of conformal structures by reduction to the relevant results of [BEGr]. In [FG], the authors conjectured that when n is odd, all scalar conformal invariants arise as Weyl invariants constructed from the ambient metric. The second main goal of this book is to prove this together with an analogous result when n is even. These results are contained in Theorems 9.2, 9.3, and 9.4. The parabolic invariant theory needed to prove these results was developed in [BEGr], including the observation of the existence of exceptional invariants. But substantial work is required to reduce the theorems in the chapter to the results of [BEGr]. To understand this, it briefly reviews how Weyl's characterization of scalar Riemannian invariants is proved.

Keywords:   conformal geometry, ambient metric, parabolic invariant theory, scalar invariants, Weyl invariants

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