The Penrose transform in quaternionic geometry

TL;DR

This paper explores the Penrose transform within quaternionic geometry, focusing on quaternionic objects with twistor spaces that are complex manifolds containing families of embedded Riemann spheres with positive normal bundles.

Contribution

It introduces a new perspective on the Penrose transform for quaternionic objects with specific twistor space structures involving Riemann spheres.

Findings

Established a correspondence between quaternionic objects and complex manifolds with Riemann spheres.

Extended the Penrose transform framework to new classes of quaternionic geometries.

Abstract

We study the Penrose transform for the `quaternionic objects' whose twistor spaces are complex manifolds endowed with locally complete families of embedded Riemann spheres with positive normal bundles.