The Geodesic X-ray Transform with a GL (n, C)-Connection
JOURNAL OF GEOMETRIC ANALYSIS
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Monard, F., & Paternain, G. (2020). The Geodesic X-ray Transform with a GL (n, C)-Connection. JOURNAL OF GEOMETRIC ANALYSIS, 30 (3), 2515-2557. https://doi.org/10.1007/s12220-017-9931-z
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numerical illustrations.
Geodesic X-ray transform, Connection, Scattering data
External DOI: https://doi.org/10.1007/s12220-017-9931-z
This record's URL: https://www.repository.cam.ac.uk/handle/1810/268504