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The Ambient Metric
Author: Charles Fefferman

ISBN: 9780691153148
Format: Paperback
Number Of Pages: 128
Published: 16 November 2011
Country of Publication: US
Dimensions (cm): 22.9 x 15.2 x 0.7
Description:


This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric inn+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincare metric, a metric inn+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.


The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincare metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincare metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their f...

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