INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM

Abstract

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.