On conformally covariant powers of the Laplacian

Understand

We propose and discuss recursive formulas for conformally covariant powers $P_{2N}$ of the Laplacian (GJMS-operators).

• For locally conformally flat metrics, these describe the non-constant part of any GJMS-operator as the sum of a certain linear combination of compositions of lower order GJMS-operators (primary part) and a second-order operator which is defined by the Schouten tensor (secondary part).
• We complete the description of GJMS-operators by proposing and discussing recursive formulas for their constant terms, i.e., for Branson's $Q$-curvatures, along similar lines.
• We confirm the picture in a number of cases.