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arXiv · 1707.01343

Tensor tomography in periodic slabs

Joonas Ilmavirta·Gunther Uhlmann
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Abstract

The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless $n=0$. We characterize the kernel of the geodesic X-ray transform for $L^2$-regular $m$-tensors for any $m\geq0$. The characterization extends to more general manifolds, twisted slabs, including the M\"obius strip as the simplest example.

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Joonas Ilmavirta, Gunther Uhlmann. 2017-07-05. Tensor tomography in periodic slabs. https://arxiv.org/abs/1707.01343

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