The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910835115294720 |
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| author | Grebnev, Haim |
| author_facet | Grebnev, Haim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09408 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces Grebnev, Haim Differential Geometry 34A55 (Primary) 53A35 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. |
| title | The Non-Abelian X-Ray Transform on Asymptotically Hyperbolic Spaces |
| topic | Differential Geometry 34A55 (Primary) 53A35 |
| url | https://arxiv.org/abs/2312.09408 |