Holographic formula for Q-curvature

Abstract

This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When specialized to the conformally flat case, the holographic formula expresses Q-curvature as a multiple of the Pfaffian and the divergence of a natural one-form. The paper also outlines the relation between holographic formulae for Q-curvature and a new theory of conformally covariant families of differential operators due to the second author.

13 pages

References in corpus (2)

• The Ambient Obstruction Tensor and Q-Curvature
• Extended obstruction tensors and renormalized volume coefficients

Cited by in corpus (5)

• Conformal Metrics with Constant Q-Curvature
• Holographic formula for the determinant of the scattering operator in thermal AdS
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Extended obstruction tensors and renormalized volume coefficients
• On the recursive structure of Branson's Q-curvature