Revista Matemática Iberoamericana


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Volume 31, Issue 1, 2015, pp. 303–312
DOI: 10.4171/RMI/835

Published online: 2015-03-05

On the relation between conformally invariant operators and some geometric tensors

Paolo Mastrolia[1] and Dario D. Monticelli[2]

(1) Università degli Studi di Milano, Italy
(2) Università degli Studi di Milano, Italy

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 $Q$-curvature, the Paneitz operator and the Schouten tensor, and with the elementary conformal tensors $\{T^u_{m,\alpha}\}$ and $\{X^u_{m,\mu}\}$ on Euclidean space introduced in [7] and [6].

Keywords: Fully nonlinear higher order equations, conformally invariant operators, Schouten tensor, Paneitz operator, $Q$-curvature, elementary conformal tensors

Mastrolia Paolo, Monticelli Dario: On the relation between conformally invariant operators and some geometric tensors. Rev. Mat. Iberoamericana 31 (2015), 303-312. doi: 10.4171/RMI/835