Twistor spaces on foliated manifolds

TL;DR

This paper develops the theory of twistor spaces on foliated manifolds, constructing the twistor space of the normal bundle and extending classical results to foliated and orbifold contexts.

Contribution

It introduces a framework for twistor theory on foliated manifolds and derives foliated and orbifold versions of classical holomorphic mapping results.

Findings

Constructed the twistor space of the normal bundle on foliated manifolds.

Extended classical holomorphic mapping results to foliated and orbifold settings.

Demonstrated that classical twistor constructions lead to foliated objects.

Abstract

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitable defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.