The inverse Penrose transform on Riemannian twistor spaces

TL;DR

This paper provides an explicit description of the inverse Penrose transform on Riemannian twistor spaces, linking solutions of field equations to cohomology representatives via the Dirac operator and conformally invariant Laplacian.

Contribution

It introduces a new explicit method to construct Dolbeault representatives from solutions of field equations on the base manifold.

Findings

Explicit inverse Penrose transform formula on Riemannian twistor spaces

Construction of Dolbeault representatives from field solutions

Connection between Dirac operator, Laplacian, and cohomology

Abstract

With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is constructed from a solution of the field equation on the base manifold.