Holography of Higher Codimension Submanifolds: Riemannian and Conformal

We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal bundle. Qualitatively new behavior is observed in the higher-codi...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2025
Hauptverfasser: Blitz, Samuel, Šilhan, Josef
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212889
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Holography of Higher Codimension Submanifolds: Riemannian and Conformal. Samuel Blitz and Josef Šilhan. SIGMA 21 (2025), 002, 41 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal bundle. Qualitatively new behavior is observed in the higher-codimension case, giving rise to new invariants that obstruct the order-by-order construction of unit-defining maps. In the conformal setting, a novel invariant (that vanishes in codimension 1) is realized as the leading transverse-order term appearing in a holographically-constructed Willmore invariant. Using the same tools, we also investigate formal solutions to extension problems off an embedded submanifold.
ISSN:1815-0659