Holographic formula for Q-curvature

Details Holographic formula for Q-curvature Holographic formula for Q-curvature

2007-04-13

arxiv.org/abs/0704.1673v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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