The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces

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.

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