Holography of Higher Codimension Submanifolds: Riemannian and Conformal
Differential Geometry
2025-01-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2405.07692,
title = {Holography of Higher Codimension Submanifolds: Riemannian and Conformal},
author = {Samuel Blitz and Josef Šilhan},
journal= {arXiv preprint arXiv:2405.07692},
year = {2025}
}