# Tensor tomography on Cartan-Hadamard manifolds

## TL;DR

This paper proves the injectivity of the geodesic X-ray transform on Cartan-Hadamard manifolds for functions and tensor fields of any order, extending previous results to higher dimensions and decay conditions.

## Contribution

It extends solenoidal injectivity results of the geodesic X-ray transform to higher dimensions and tensor fields on Cartan-Hadamard manifolds with specific decay assumptions.

## Key findings

- Proves injectivity of the geodesic X-ray transform for tensor fields.
- Extends previous results to dimensions n ≥ 3.
- Handles functions with exponential or polynomial decay.

## Abstract

We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016) to dimensions $n \geq 3$ and to the case of tensor fields of any order.