Charles Fefferman and C. Robin Graham
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153131
- eISBN:
- 9781400840588
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153131.003.0009
- Subject:
- Mathematics, Geometry / Topology
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, ...
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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.Less
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.
