INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal $\textit{m}$-tensors. We work with compact simple manifolds, but several of our results apply to non-trapping manifolds with strictly convex boundary.This is the final version of the article. It first appeared from Mathematical Science Publishers via https://doi.org/10.2140/apde.2016.9.190