Concept# Paneitz operator

Summary

In the mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension n. It is named after Stephen Paneitz, who discovered it in 1983, and whose preprint was later published posthumously in .
In fact, the same operator was found earlier in the context of conformal supergravity by E. Fradkin and A. Tseytlin in 1982
(Phys Lett B 110 (1982) 117 and Nucl Phys B 1982 (1982) 157 ).
It is given by the formula
:P = \Delta^2 - \delta \left{(n-2)J - 4V\cdot\right}d + (n-4)Q
where Δ is the Laplace–Beltrami operator, d is the exterior derivative, δ is its formal adjoint, V is the Schouten tensor, J is the trace of the Schouten tensor, and the dot denotes tensor contraction on either index. Here Q is the scalar invariant
:(-4|V|^2+nJ^2+2\Delta J)/4,
where Δ is the positive Laplacian. In four dimensions this yields the Q-curvature.
The operator is especially important

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

No results

Related concepts

No results

Related lectures

No results

Related units

No results

Related courses

Related people

No results

No results