Conformally invariant powers of the Laplacian. I: Existence. (English) Zbl 0726.53010

Graham, C. Robin; Jenne, Ralph; Mason, Lionel J.; Sparling, George A. J.

J. Lond. Math. Soc., II. Ser. 46, No. 3, 557-565 (1992).

A geometric derivation is given of a family of scalar conformally invariant differential operators on conformal densities with leading part a power of the Laplacian. The derivation produces an operator for each positive integral power in odd dimensions, but only for finite range of powers in even dimensions. The operators are derived from the Laplacian in the ambient metric of Fefferman-Graham via extension.
For Part II see [ibid. 46, No. 3, 566–576 (1992; Zbl 0726.53011)].

Reviewer: C. Robin Graham

MSC:

53A30	Conformal differential geometry (MSC2010)
58J70	Invariance and symmetry properties for PDEs on manifolds

Keywords:

conformally invariant differential operators; conformal densities; Laplacian

Citations:

Zbl 0726.53011