Inverting the local geodesic ray transform of higher rank tensors

Abstract

Consider a Riemannian manifold in dimension with a strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related to elastic qP-wave tomography. Under the condition that the manifold can be foliated with a continuous family of strictly convex hypersurfaces, the local invertibility implies a global result. One can straightforwardedly adapt the proof to show similar results for tensor fields of arbitrary rank.