The Ambient Obstruction Tensor and Q-Curvature

Abstract

It is shown that the variational derivative of the integral of Branson's Q-curvature is the ambient obstruction tensor of Fefferman-Graham. A classification of irreducible conformally invariant tensors modulo quadratic and higher degree terms in curvature is established.

12 pages

Cited by in corpus (31)

• Entanglement entropy of black holes
• Explicit formulas for GJMS-operators and $Q$-curvatures
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
• Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
• Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem
• On the AdS stability problem
• Holographic Description of Gravitational Anomalies
• Yang-Mills detour complexes and conformal geometry
• Obstruction Tensors in Weyl Geometry and Holographic Weyl Anomaly
• On conformally covariant powers of the Laplacian
• Variation of total Q-prime curvature on CR manifolds
• Non-singular, vacuum, stationary space-times with a negative cosmological constant
• A sub-product construction of Poincare-Einstein metrics
• A GJMS construction for 2-tensors and the second variation of the total Q-curvature
• Ambient constructions for Sasakian $\eta$-Einstein manifolds
• Holographic formula for Q-curvature
• On the structure of asymptotically de Sitter and anti-de Sitter spaces
• Unique continuation and extensions of Killing vectors at boundaries for stationary vacuum space-times
• Extended obstruction tensors and renormalized volume coefficients
• Variational Principles for Natural Divergence-free Tensors in Metric Field Theories
• AdS Chern-Simons Gravity induces Conformal Gravity
• Residue families, singular Yamabe problems and extrinsic conformal Laplacians
• Rigidity of conformal functionals on spheres
• Geometric Asymptotics and Beyond
• Boundary regularity of conformally compact Einstein metrics
• Conformal Dilaton Gravity: Classical Noninvariance Gives Rise To Quantum Invariance
• Les applications conforme-harmoniques
• Asymptotics of ACH-Einstein metrics
• Boundary Estimate of Asymptotically Hyperbolic Einstein Manifolds of Even Dimension
• One-loop divergences in 7D Einstein and 6D Conformal Gravities
• Pontrjagin forms and invariant objects related to the Q-curvature