The Attenuated Magnetic Ray Transform on Surfaces

Abstract

It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction. Furthermore, the scattering relation determines the connection and Higgs field modulo a gauge transformation. We extend the results obtained therein to the case of magnetic geodesics. In addition, we provide an application to tensor tomography in the magnetic setting, along the lines of [Pa2].

arXiv comment20 pages; minor revisions to reflect published version, to appear in Inverse Problems and Imaging. arXiv admin note: text overlap with arXiv:1108.1118 by other authors