The Ambient Metric (AM-178)

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book The Ambient Metric (AM-178) by Charles Fefferman, C. Robin Graham, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Charles Fefferman, C. Robin Graham ISBN: 9781400840588
Publisher: Princeton University Press Publication: November 14, 2011
Imprint: Princeton University Press Language: English
Author: Charles Fefferman, C. Robin Graham
ISBN: 9781400840588
Publisher: Princeton University Press
Publication: November 14, 2011
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book The Theory of Taxation and Public Economics by Charles Fefferman, C. Robin Graham
Cover of the book Parrots of the World by Charles Fefferman, C. Robin Graham
Cover of the book Biomedical Odysseys by Charles Fefferman, C. Robin Graham
Cover of the book Philosophical Myths of the Fall by Charles Fefferman, C. Robin Graham
Cover of the book Modern Political Science by Charles Fefferman, C. Robin Graham
Cover of the book That Eminent Tribunal by Charles Fefferman, C. Robin Graham
Cover of the book The Making of Martin Luther by Charles Fefferman, C. Robin Graham
Cover of the book Reconceiving Infertility by Charles Fefferman, C. Robin Graham
Cover of the book After Hegel by Charles Fefferman, C. Robin Graham
Cover of the book Greece--a Jewish History by Charles Fefferman, C. Robin Graham
Cover of the book Euripides and the Politics of Form by Charles Fefferman, C. Robin Graham
Cover of the book The Corruption Cure by Charles Fefferman, C. Robin Graham
Cover of the book Iraq by Charles Fefferman, C. Robin Graham
Cover of the book Nonlinear Dynamical Systems and Control by Charles Fefferman, C. Robin Graham
Cover of the book Trade Unions and the State by Charles Fefferman, C. Robin Graham
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy