Develops and applies a theory of the ambient metric in conformal geometry. This title includes the derivation of the ambient obstruction tensor and an analysis of the cases of conformally flat and conformally Einstein spaces. It concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature. Series: Annals of Mathematics Studies. Num Pages: 128 pages, black & white illustrations. BIC Classification: PBMW. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 233 x 156 x 10. Weight in Grams: 204. . 2011. Paperback. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verk�ufers V9780691153148

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Bibliografische Details

Titel: The Ambient Metric (AM-178)
Verlag: Princeton University Press
Erscheinungsjahr: 2011
Sprache: Englisch
ISBN-10: 0691153140
ISBN-13: 9780691153148
Einband: Softcover
Zustand: New

�ber diesen Titel

Inhaltsangabe

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.

�ber die Autorin bzw. den Autor

Charles Fefferman is the Herbert E. Jones, Jr., '43 University Professor of Mathematics at Princeton University. C. Robin Graham is professor of mathematics at the University of Washington.

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