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 recently constructed on the Euclidean space.
On the relation between conformally invariant operators and some geometric tensors / P. Mastrolia, D. Monticelli. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 31:1(2015), pp. 303-312. [10.4171/RMI/835]
On the relation between conformally invariant operators and some geometric tensors
P. MastroliaPrimo
;D. MonticelliUltimo
2015
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 Q-curvature, the Paneitz operator and the Schouten tensor, and with the elementary conformal tensors recently constructed on the Euclidean space.File | Dimensione | Formato | |
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