JournalsrmiVol. 31, No. 1pp. 303–312

On the relation between conformally invariant operators and some geometric tensors

  • Paolo Mastrolia

    Università degli Studi di Milano, Italy
  • Dario D. Monticelli

    Università degli Studi di Milano, Italy
On the relation between conformally invariant operators and some geometric tensors cover
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Abstract

In this note we introduce and study some new tensors on general Riemannian manifolds which provide a link between the geometry of the underlying manifold and conformally invariant operators (up to order four). We study some of their properties and their relations with well-known geometric objects, such as the scalar curvature, the QQ-curvature, the Paneitz operator and the Schouten tensor, and with the elementary conformal tensors {Tm,αu}\{T^u_{m,\alpha}\} and {Xm,μu}\{X^u_{m,\mu}\} on Euclidean space introduced in [7] and [6].

Cite this article

Paolo Mastrolia, Dario D. Monticelli, On the relation between conformally invariant operators and some geometric tensors. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 303–312

DOI 10.4171/RMI/835