Abstract
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric -tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal -tensors. We work with compact simple manifolds, but several of our results apply to nontrapping manifolds with strictly convex boundary.
Citation
Gabriel P. Paternain. Hanming Zhou. "Invariant distributions and the geodesic ray transform." Anal. PDE 9 (8) 1903 - 1930, 2016. https://doi.org/10.2140/apde.2016.9.1903
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