Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors

Abstract

Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\ge 3$ and the mixed ray transform of $2+2$ tensors for $n=3$. When the manifold admits a strictly convex function, this local invertibility result leads to global invertibility.