The inversion of the X-ray Transform on a Compact Symmetric Space

TL;DR

This paper presents an explicit inversion formula for the X-ray transform on compact symmetric spaces, utilizing geometric properties of geodesics and totally geodesic spheres to achieve the inversion.

Contribution

It introduces a novel explicit inversion formula for the X-ray transform on compact symmetric spaces based on geometric conjugacy properties.

Findings

Explicit inversion formula derived for the X-ray transform

Utilizes conjugacy of geodesics and geodesic spheres in the proof

Provides a geometric approach to inversion on symmetric spaces

Abstract

The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M, proved in Math. Ann. 165 (1966), 309--317.