Attenuated tensor tomography on simple surfaces

TL;DR

This paper investigates the injectivity of the attenuated tensor X-ray transform on simple surfaces, demonstrating that it is injective up to natural obstructions when applied to pairs of tensors.

Contribution

It extends the understanding of tensor tomography by establishing injectivity results for the attenuated transform involving complex functions and 1-forms on simple surfaces.

Findings

Injectivity of the attenuated tensor X-ray transform modulo natural obstruction

Extension of tensor tomography results to complex functions and 1-forms

Applicability to simple surfaces in geometric analysis

Abstract

In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the natural obstruction.