The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces
Differential Geometry
2025-02-20 v4
Abstract
In this paper we formulate and prove a gauge equivalence for unitary connections and skew-Hermitian Higgs fields of suitable regularity that are mapped to the same function under the non-abelian X-ray transform on nontrapping asymptotically hyperbolic spaces with negative curvature and no nontrivial twisted conformal Killing tensor fields with certain regularity. If one furthermore fixes such a connection with zero curvature, a corollary provides an injectivity result for the non-abelian X-ray transform over skew-Hermitian Higgs fields.
Cite
@article{arxiv.2312.09408,
title = {The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces},
author = {Haim Grebnev},
journal= {arXiv preprint arXiv:2312.09408},
year = {2025}
}
Comments
59 pages. In version 4 we 1) fixed which connection has no nontrivial CKTs in the main theorem and its proof 2) expanded/improved exposition 3) fixed typos