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

## TL;DR

This paper establishes new support theorems and an injectivity result for integral moments of symmetric m-tensor fields on simple Riemannian manifolds, extending previous Helgason-type theorems using integral moments.

## Contribution

It generalizes a Helgason-type support theorem for integral moments of tensor fields and proves an injectivity result using the first m+1 integral moments.

## Key findings

- Support theorems for integral moments of tensor fields
- Injectivity result for integral moments
- Extension of Helgason-type theorems

## Abstract

In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generalize a Helgason type support theorem proven by Krishnan and Stefanov in "A support theorem for the geodesic ray transform of symmetric tensor fields", Inverse Problems and Imaging, 3(3):453-464,2009. We use this extended result along with the first m+1-integral moments of a m-tensor field to prove the aforementioned results.