Extrinsic Paneitz operators and Q-curvatures for hypersurfaces

2021/10/10 by Andreas Juhl, Juhl, Andreas
Mathematics · Physics and Astronomy · #35J30 #53B20 #53B25 #53C18 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:35J30 #msc:53B20 #msc:53B25 #msc:53C18 #msc:58J50

paper · pdf · doi:10.48550/arxiv.2110.04838

9 pages, research announcement, corrected misprints and minor revision of some details

openalex publication_date 2021/10/10 · arxiv created 2022/04/12 · arxiv updated 2022/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any hypersurface of a Riemannian manifold, recent works introduced the notions of extrinsic conformal Laplacians and extrinsic Q-curvatures. Here we announce explicit formulas for the extrinsic Paneitz operators P₄ and the corresponding extrinsic Q-curvatures for totally umbilic hypersurfaces in any dimension. Moreover, we state explicit formulas for the critical extrinsic P₄ and the total integral of the critical extrinsic Q₄ in the general case. This integral is a global conformal invariant. Finally, we establish an analog of the Alexakis-Deser-Schwimmer decomposition of the critical extrinsic Q₄.

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