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Item Title:

The Ambient Metric (AM-178) (Annals of Mathematics Studies)- Charles F

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Item Condition: New
Current Time:24 Oct 17 06:49:47
Time & Date displayed is forUnited States - EDT
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Item Specifics - Books ISBN : 9780691153131
Author : Charles Fefferman C. Robin Graham
45.41 15578342 The Ambient Metric (AM-178) (Annals of Mathematics Studies) http://medium.snazal.com/?9780691153131 http://large.snazal.com/?9780691153131 Charles Fefferman C. Robin Graham 9780691153131 9780691153131
Lot # 15578342
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Title: The Ambient Metric (AM-178) (Annals of Mathematics Studies)

Author(s): Charles Fefferman C. Robin Graham
Publisher:
ISBN: 9780691153131
Sku Code: 9780691153131
Media > Books
The Ambient Metric (AM-178) (Annals of Mathematics Studies)
Description:
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. Self-dual 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.

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