Holography of Higher Codimension Submanifolds: Riemannian and Conformal
| Autoři | |
|---|---|
| Rok publikování | 2025 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Symmetry, Integrability and Geometry: Methods and Applications |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://www.emis.de/journals/SIGMA/2025/002/ |
| Doi | http://dx.doi.org/10.3842/SIGMA.2025.002 |
| Klíčová slova | Riemannian geometry; conformal geometry; submanifold embeddings; holo- graphy |
| 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-co dimension 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 co dimension 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. |
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