Zero-Energy Fields on Complex Projective Space

TL;DR

This paper investigates the X-ray transform on complex projective space with the Fubini-Study metric, identifying the kernel when acting on symmetric tensor fields, which advances understanding of integral geometry in complex manifolds.

Contribution

It precisely characterizes the kernel of the X-ray transform on complex projective space for symmetric tensor fields, a novel result in integral geometry.

Findings

Kernel of the X-ray transform explicitly identified

Enhanced understanding of integral geometry on complex manifolds

Potential applications in geometric analysis and tomography

Abstract

We consider complex projective space with its Fubini-Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetric tensor fields.