Compatible almost complex structures on twistor spaces and their Gray-Hervella classes

TL;DR

This paper classifies the Gray-Hervella classes of compatible almost complex structures on twistor spaces of oriented Riemannian four-manifolds, extending understanding of their geometric properties.

Contribution

It provides a detailed classification of Gray-Hervella classes for these structures, offering new insights into their geometric and complex-analytic features.

Findings

Identification of Gray-Hervella classes for twistor space structures

Characterization of compatibility conditions for almost complex structures

Extension of previous classifications to new geometric contexts

Abstract

In this paper we determine the Gray-Hervella classes of the compatible almost complex structures on the twistor spaces of oriented Riemannian four-manifolds considered by G. Deschamps