Conformally invariant powers of the Laplacian -- A complete non-existence theorem

dc.creatorGover, A. Rod
dc.creatorHirachi, Kengo
dc.date2003-04-07
dc.date2003-12-10
dc.date.accessioned2026-07-07T06:33:33Z
dc.date.available2026-07-07T06:33:33Z
dc.descriptionWe show that on conformal manifolds of even dimension $n\geq 4$ there is no conformally invariant natural differential operator between density bundles with leading part a power of the Laplacian $Δ^{k}$ for $k>n/2$. This shows that a large class of invariant operators on conformally flat manifolds do not generalise to arbitrarily curved manifolds and that the theorem of Graham, Jenne, Mason and Sparling, asserting the existence of curved version of $Δ^k$ for $1\le k\le n/2$, is sharp.
dc.description18 pages; Minor changes and typographical corrections throughout article; To appear in Jour. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0304082
dc.identifierhttp://arxiv.org/abs/math/0304082
dc.identifierJ.Am.Math.Soc. 17 (2004) 389-405
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99229
dc.subjectDifferential Geometry
dc.subject53A30 (Primary); 53A55, 35Q99(Secondary)
dc.titleConformally invariant powers of the Laplacian -- A complete non-existence theorem
dc.typetext

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