On the relation between conformally invariant operators and some geometric tensors

• Paolo Mastrolia ^[1] ; Dario D. Monticelli ^[1]
  1. [1] University of Milan

     University of Milan

     Milán, Italia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 1, 2015, págs. 303-312
• Idioma: inglés
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• Resumen

  • 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 {Tum,α} and {Xum,μ} on Euclidean space introduced in [7] and [6].