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Könyv Ambient Metric (AM-178) Charles Fefferman

Ambient Metric (AM-178)

Szerző: Charles Fefferman, C. Robin Graham
Nyelv: Angol
Kötés: Puha kötésű
Kiadó: Princeton University Press
Elérhetőség: Beszállítói készleten
Küldés 14-21 napon belül
35 337 Ft
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Loren...

Információk a könyvről

Szerző
Charles Fefferman, C. Robin Graham
Nyelv
Angol
Kötés
Könyv - Puha kötésű
Kiadva
2011
oldal
128
EAN
9780691153148
ISBN
0691153140
Enbook ID
04641932
Kiadó
Princeton University Press
Súly
204
Méretek
156 x 233 x 10

Teljes leírás

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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