# Generalized metrics and generalized twistor spaces

## TL;DR

This paper extends the twistor construction to manifolds with generalized metrics, defining generalized twistor spaces and analyzing their structures and integrability conditions within generalized geometry.

## Contribution

It introduces the concept of generalized twistor spaces for manifolds with generalized metrics and studies their natural structures and integrability conditions.

## Key findings

- Existence of natural generalized almost complex structures on these spaces
- Conditions for integrability of these structures
- Intrinsic isomorphisms of generalized twistor spaces

## Abstract

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the manifold compatible with the given generalized metric. This space admits natural generalized almost complex structures whose integrability conditions are found in the paper. An interesting feature of the generalized twistor spaces discussed in it is the existence of intrinsic isomorphisms.