Extrinsic Paneitz Operators and Q-Curvatures for Hypersurfaces
Extrinsic Paneitz Operators and Q-Curvatures for Hypersurfaces
For any hypersurface $M$ of a Riemannian manifold $X$, recent works introduced the notions of extrinsic conformal Laplacians and extrinsic $Q$-curvatures. We derive explicit formulas for the extrinsic version ${\bf P}_4$ of the Paneitz operator and the corresponding extrinsic fourth-order $Q$-curvature ${\bf Q}_4$ in general dimensions. In the critical dimension …