Twistor theory, complex homogeneous manifolds and $G$-structures

TL;DR

This paper demonstrates that twistor methods can construct irreducible 1-flat G-structures and torsion-free affine connections with irreducible holonomy, linking complex geometry and differential structures.

Contribution

It introduces a twistor-based approach to constructing specific geometric structures and connections, expanding the toolkit for differential geometry and complex manifold analysis.

Findings

Irreducible analytic 1-flat G-structures can be constructed via twistor methods.

Analytic torsion-free affine connections with irreducible holonomy are also constructible through twistor techniques.

The work bridges twistor theory with the theory of G-structures and affine connections.

Abstract

It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.