Holography of Higher Codimension Submanifolds: Riemannian and Conformal

Autor:	Blitz, Samuel, Šilhan, Josef
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry 53C18 53A55 53C21 58J32
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
Externí odkaz:	http://arxiv.org/abs/2405.07692 Zobrazit plný text záznamu View this record from Arxiv