Annales Henri Poincaré

, Volume 15, Issue 4, pp 679–705 | Cite as

Conformal Operators on Weighted Forms; Their Decomposition and Null Space on Einstein Manifolds

Article

Abstract

There is a class of Laplacian like conformally invariant differential operators on differential forms \({L^\ell_k}\) which may be considered as the generalisation to differential forms of the conformally invariant powers of the Laplacian known as the Paneitz and GJMS operators. On conformally Einstein manifolds we give explicit formulae for these as factored polynomials in second-order differential operators. In the case that the manifold is not Ricci flat we use this to provide a direct sum decomposition of the null space of the \({L^\ell_k}\) in terms of the null spaces of mutually commuting second-order factors.

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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand
  2. 2.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  3. 3.Institute of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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