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arXiv · 2312.09408

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

Haim Grebnev
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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.

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Haim Grebnev. 2023-12-15. The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces. https://arxiv.org/abs/2312.09408

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