Espaces de twisteurs des structures complexes g\'en\'eralis\'ees

TL;DR

This paper extends Penrose's twistor space concept using generalized complex structures, adapting Atiyah-Hitchin-Singer integrability, and establishing new links between differential and complex geometry, also generalizing Bredthauer's work.

Contribution

It introduces a generalized framework for twistor spaces via complex structures, broadening their applicability and connecting different geometric theories.

Findings

Extended twistor space definitions using generalized complex structures

Adapted integrability conditions from Atiyah-Hitchin-Singer

Established new correspondences between differential and complex geometry

Abstract

The aim of this article is to use generalized complex structures in order to extend the definition of twistor spaces given by Penrose. We will adapt the integrability result of Atiyah, Hitchin and Singer. We will deduce new correspondences betwenn differential geometry and (generalized) complex geometry. In the last section we will show how these results generalized Bredthauer's work.