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: https://doi.org/10.1093/imrn/rnad053.

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Work Title Curved Versions of the Ovsienko–Redou Operators
Access
Open Access
Creators
  1. Jeffrey S. Case
  2. Yueh-Ju Lin
  3. Wei Yuan
Keyword
  1. Ovsienko–Redou operator
  2. Conformally invariant bidifferential operator
  3. Conformally invariant operator
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. International Mathematics Research Notices
Publication Date March 28, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1093/imrn/rnad053
Deposited January 23, 2024

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