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 -curvature, the Paneitz operator and the Schouten tensor, and with the elementary conformal tensors and on Euclidean space introduced in  and .
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. 303–312DOI 10.4171/RMI/835