The ambient metric
 Responsibility
 Charles Fefferman, C. Robin Graham.
 Language
 English.
 Imprint
 Princeton, N.J. : Princeton University Press, 2012.
 Physical description
 111 p. : ill. ; 25 cm.
 Series
 Annals of mathematics studies ; no. 178.
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Math & Statistics Library

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QA1 .A665 NO.178

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QA1 .A665 NO.178
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Creators/Contributors
 Author/Creator
 Fefferman, Charles, 1949
 Contributor
 Graham, C. Robin, 1954
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Chapter 1. Introduction 1 Chapter 2. Ambient Metrics 9 Chapter 3. Formal Theory 17 Chapter 4. Poincar'e Metrics 42 Chapter 5. Selfdual Poincar'e Metrics 50 Chapter 6. Conformal Curvature Tensors 56 Chapter 7. Conformally Flat and Conformally Einstein Spaces 67 Chapter 8. Jet Isomorphism 82 Chapter 9. Scalar Invariants 97 Bibliography 107 Index 113.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 Poincar 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 obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincar metrics are introduced and shown to be equivalent to the ambient formulation. Selfdual Poincar 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 fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2012
 Series
 Annals of mathematics studies ; no. 178
 ISBN
 9780691153131 (hardback : acidfree paper)
 0691153132 (hardback : acidfree paper)
 9780691153148 (pbk. : acidfree paper)
 0691153140 (pbk. : acidfree paper)