Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field

In this work, we show an injectivity result and support theorems for integral moments of a symmetric m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of symmetric m-tensor fields were first introduced by Sharafutdinov. First we generalize a Helgason type support theorem proven by Krishnan and Stefanov (Inverse Probl Imaging 3(3):453-464, 2009). We use this extended result along with the first integral moments of a symmetric m-tensor field to prove the aforementioned results.