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 language | English (US) |
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Pages (from-to) | 16904-16929 |
Number of pages | 26 |
Journal | International Mathematics Research Notices |
Volume | 2023 |
Issue number | 19 |
DOIs | |
State | Published - Oct 1 2023 |
All Science Journal Classification (ASJC) codes
- General Mathematics