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Conformally invariant powers of the Laplacian. II: Nonexistence. (English) Zbl 0726.53011
It is shown that there is no natural differential operator on 4-dimensional pseudo-Riemannian manifolds which is conformally invariant when acting on conformal densities and which has the same principal part as Laplacian cubed. Also a formula is derived for a conformally invariant fourth-order operator on weighted 1-forms in four dimensions which has been asserted not to exist.
For Part I see [ibid. 46, No. 3, 557–565 (1992; Zbl 0726.53010)].
Reviewer: C. Robin Graham

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