Holography of Higher Codimension Submanifolds: Riemannian and Conformal
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915089890672640 |
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| author | Blitz, Samuel Šilhan, Josef |
| author_facet | Blitz, Samuel Šilhan, Josef |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holography of Higher Codimension Submanifolds: Riemannian and Conformal Blitz, Samuel Šilhan, Josef Differential Geometry 53C18, 53A55, 53C21, 58J32 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. |
| title | Holography of Higher Codimension Submanifolds: Riemannian and Conformal |
| topic | Differential Geometry 53C18, 53A55, 53C21, 58J32 |
| url | https://arxiv.org/abs/2405.07692 |