The attenuated magnetic ray transform on surfaces

Gareth Ainsworth

doi:10.3934/ipi.2013.7.27

Article Contents

2013, Volume 7, Issue 1: 27-46. Doi: 10.3934/ipi.2013.7.27

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The attenuated magnetic ray transform on surfaces

Gareth Ainsworth^1,

1.
Trinity College, Cambridge, CB2 1TQ

Received: May 31, 2012

Revised: September 30, 2012

Published: January 2013

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Abstract

It has been shown in [10] 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 [11].

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Mathematics Subject Classification: Primary: 53C22.

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References

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