On Branson’s $Q$-curvature of order eight

On Branson’s Q-curvature of Order Eight

We prove universal recursive formulas for Branson’s Q-curvature of order eight in terms of lower-order Q-curvatures, lower-order GJMSoperators and holographic coefficients. The results confirm a special case of a conjecture in [On conformally covariant powers of the Laplacian, arXiv:0905.3992v3].

On semifields of order q

The semifields of order q which are two-dimensional over their left nucleus and six-dimensional over their center have been geometrically partitioned into six classes by using the associated linear sets in PG(3, q). One of these classes has been partitioned further (again geometrically) into three subclasses. In this paper the generic multiplication is determined for each of these three subclas...

What Is Q-curvature?

Branson’s Q-curvature is now recognized as a fundamental quantity in conformal geometry. We outline its construction and present its basic properties.

Q-curvature and Poincaré Metrics

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

On a Fourth Order Curvature Invariant