Tensor tomography on Cartan-Hadamard manifolds
Lehtonen, J., Railo, J., & Salo, M. (2018). Tensor tomography on Cartan-Hadamard manifolds. Inverse Problems, 34 (4), 044004. doi:10.1088/1361-6420/aaaf85
Published inInverse Problems
© 2018 IOP Publishing Ltd. This is a final draft version of an article whose final and definitive form has been published by IOP Publishing Ltd. Published in this repository with the kind permission of the publisher.
We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions $n \geqslant 3$ and to the case of tensor fields of any order.