Integrable Complex Structures on Twistor Spaces

TL;DR

This paper explores the construction of integrable complex structures on twistor spaces over complex manifolds, demonstrating their natural existence in various geometric contexts and constructing compatible structures with equal torsions.

Contribution

It introduces integrable complex structures on twistor spaces and shows their natural occurrence in generalized Kahler, SKT, and strong HKT manifolds, including a new metric and compatible structures in the HKT case.

Findings

Twistor spaces associated with certain manifolds admit natural complex structures.

Constructed a metric and three compatible complex structures with equal torsions in the strong HKT case.

Established the integrability of these complex structures on twistor spaces.

Abstract

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three compatible complex structures on the twistor space that have equal torsions.