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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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Poincaré Metrics

Poincaré Metrics

Chapter Four Poincaré Metrics
The Ambient Metric (AM-178)

Charles Fefferman

C. Robin Graham

Princeton University Press

This chapter considers the formal theory for Poincaré metrics associated to a conformal manifold (M, [g]). It shows that even Poincaré metrics are in one-to-one correspondence with straight ambient metrics, if both are in normal form. Thus, the formal theory for Poincaré metrics is a consequence of the results of Chapter 3. The derivation of a Poincaré metric from an ambient metric was described in [FG], and the inverse construction of an ambient metric as the cone metric over a Poincaré metric was given in § 5 of [GrL].

Keywords:   conformal geometry, ambient metric, Poincaré metrics, conformal manifold

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