A01=C. Robin Graham
A01=Charles Fefferman
Ambient space
Analytic function
Asymptote
Author_C. Robin Graham
Author_Charles Fefferman
Calculation
Category=PBMW
Change of variables
Coefficient
Computation
Conformal geometry
Conformal group
Cotton tensor
Covariant derivative
Curvature
Curvature tensor
Derivative
Diffeomorphism
Differentiable manifold
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Equivalence class
Existential quantification
Explicit formula
Fiber bundle
Formal power series
Hyperbolic space
Hypersurface
Initial condition
Interval (mathematics)
Invariant theory
Isomorphism theorem
Levi-Civita connection
Linear combination
Linearization
Local diffeomorphism
Mathematical induction
Metric tensor
Monomial
Neighbourhood (mathematics)
Order by
Orthogonal group
Pairing
Partial differential equation
Permutation
Polynomial
Pseudo-Riemannian manifold
Quadratic form
Requirement
Ricci curvature
Riemann surface
Riemannian geometry
Scalar curvature
Scientific notation
Sign convention
Smoothness
Submanifold
Subset
Summation
Symmetrization
Tangent bundle
Tangent space
Tangent vector
Taylor series
Tensor
Tensor algebra
Theorem
Trace (linear algebra)
Triangular matrix
Uniformization theorem
Vector field
Vector space
Volume form
Weyl tensor
Product details
- ISBN 9780691153148
- Weight: 198g
- Dimensions: 152 x 235mm
- Publication Date: 04 Dec 2011
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
