Curved Versions of the Ovsienko–Redou Operators

Jeffrey S. Case, Yueh Ju Lin, Wei Yuan

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)16904-16929
Number of pages26
JournalInternational Mathematics Research Notices
Volume2023
Issue number19
DOIs
StatePublished - Oct 1 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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