Curved Versions of the Ovsienko–Redou Operators

We construct a family of conformally covariant bidifferential operators on pseudo-Riemannian manifolds. Our construction is analogous to the construction of Graham–Jenne–Mason–Sparling of conformally covariant differential operators via tangential powers of the Laplacian in the Fefferman–Graham ambient space. In fact, we com pletely classify the tangential bidifferential operators on the ambient space, which are expressed purely in terms of the ambient Laplacian. This gives a curved analogue of the classification, due to Ovsienko–Redou and Clerc, of conformally invariant bidifferential operators on the sphere. As an application, we construct a large class of formally self-adjoint conformally invariant differential operators.

This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record [Curved Versions of the Ovsienko–Redou Operators. International Mathematics Research Notices (2023)] is available online at:


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Work Title Curved Versions of the Ovsienko–Redou Operators
Open Access
  1. Jeffrey S. Case
  2. Yueh-Ju Lin
  3. Wei Yuan
  1. Ovsienko–Redou operator
  2. Conformally invariant bidifferential operator
  3. Conformally invariant operator
License In Copyright (Rights Reserved)
Work Type Article
  1. International Mathematics Research Notices
Publication Date March 28, 2023
Publisher Identifier (DOI)
Deposited January 23, 2024




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Work History

Version 1

  • Created
  • Added ovsienko-redou-1.pdf
  • Added Creator Jeffrey S. Case
  • Added Creator Yueh Ju Lin
  • Added Creator Wei Yuan
  • Published
  • Updated Keyword Show Changes
    • Ovsienko–Redou operator, Conformally invariant bidifferential operator, Conformally invariant operator
  • Renamed Creator Yueh-Ju Lin Show Changes
    • Yueh Ju Lin
    • Yueh-Ju Lin
  • Updated