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The Ambient Metric (AM-178) - Princeton Scholarship Online
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The Ambient Metric (AM-178)

Charles Fefferman and C. Robin Graham


This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+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 o ... More

Keywords: conformal geometry, n+2 dimensions, Poincaré metric, Lorentz metric, ambient metric, ambient curvature, parabolic invariant theory

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780691153131
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691153131.001.0001


Affiliations are at time of print publication.

Charles Fefferman, author
Princeton University

C. Robin Graham, author
University of Washington