2007/04/13 by Graham, C. Robin, Juhl, Andreas · 1 citation
#53B20 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0704.1673
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.