Holography of Higher Codimension Submanifolds: Riemannian and Conformal
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Symmetry, Integrability and Geometry: Methods and Applications |
| MU Faculty or unit | |
| Citation | |
| web | https://www.emis.de/journals/SIGMA/2025/002/ |
| Doi | http://dx.doi.org/10.3842/SIGMA.2025.002 |
| Keywords | Riemannian geometry; conformal geometry; submanifold embeddings; holo- graphy |
| Description | 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. |
| Related projects: |