The Resource The ambient metric, Charles Fefferman, C. Robin Graham
The ambient metric, Charles Fefferman, C. Robin Graham
 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 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 obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Selfdual Poincaré 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
 Language
 eng
 Extent
 1 online resource (111 pages).
 Contents

 1. Introduction
 2. Ambient Metrics
 3. Formal Theory
 4. Poincare? Metrics
 5. Selfdual Poincare? Metrics
 6. Conformal Curvature Tensors
 7. Conformally Flat and Conformally Einstein Spaces
 8. Jet Isomorphism
 9. Scalar Invariants
 Isbn
 9781400840588
 Label
 The ambient metric
 Title
 The ambient metric
 Statement of responsibility
 Charles Fefferman, C. Robin Graham
 Language
 eng
 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 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 obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Selfdual Poincaré 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
 Cataloging source
 N$T
 Index
 index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Annals of mathematics studies
 Series volume
 no. 178
 Label
 The ambient metric, Charles Fefferman, C. Robin Graham
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 107111) and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1. Introduction  2. Ambient Metrics  3. Formal Theory  4. Poincare? Metrics  5. Selfdual Poincare? Metrics  6. Conformal Curvature Tensors  7. Conformally Flat and Conformally Einstein Spaces  8. Jet Isomorphism  9. Scalar Invariants
 http://library.link/vocab/cover_art
 https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9781400840588&userID=ebscotest&password=ebscotest
 Dimensions
 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4327146'}
 Extent
 1 online resource (111 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9781400840588
 Lccn
 2011023939
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
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