Holography of Higher Codimension Submanifolds: Riemannian and Conformal
Autor: | Blitz, Samuel, Šilhan, Josef |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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 these same tools, we also investigate the formal solutions to extension problems off of an embedded submanifold. Comment: 34 pages |
Databáze: | arXiv |
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