The matrix weighted real-analytic double fibration transforms

TL;DR

This paper introduces a real-analytic matrix-weighted double fibration transform that determines the wavefront set of vector functions and applies it to prove injectivity and uniqueness results for matrix and Higgs field transforms on real-analytic Riemannian manifolds.

Contribution

It develops a new transform that links wavefront sets to ray transforms and establishes injectivity and uniqueness results for these transforms on real-analytic manifolds.

Findings

The matrix weighted double fibration transform determines the analytic wavefront set.

The matrix weighted ray transform is injective on certain real-analytic Riemannian manifolds.

A real-analytic Higgs field can be uniquely recovered from the nonabelian ray transform.

Abstract

We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with a strictly convex boundary point.