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The Resource The ambient metric, Charles Fefferman, C. Robin Graham

The ambient metric, Charles Fefferman, C. Robin Graham

Label
The ambient metric
Title
The ambient metric
Statement of responsibility
Charles Fefferman, C. Robin Graham
Creator
Contributor
Subject
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. Self-dual 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
Member of
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
The ambient metric, Charles Fefferman, C. Robin Graham
Label
The ambient metric, Charles Fefferman, C. Robin Graham
Link
http://www.jstor.org/stable/10.2307/j.ctt7rjjg
Publication
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Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 107-111) 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. Self-dual 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=ebsco-test&password=ebsco-test
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

Library Locations

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