Twistor Theory for co-CR quaternionic manifolds and related structures

TL;DR

This paper introduces co-CR quaternionic manifolds, a broad class encompassing quaternionic and Einstein-Weyl spaces, and develops their Twistor Theory along with a heaven space construction for quaternionic-Kaehler manifolds.

Contribution

It defines co-CR quaternionic manifolds in a non-metrical setting and establishes their rich Twistor Theory and heaven space construction.

Findings

Co-CR quaternionic manifolds generalize quaternionic and Einstein-Weyl spaces.

A natural Twistor Theory is developed for these manifolds.

A heaven space construction for quaternionic-Kaehler manifolds is obtained.

Abstract

In a general and non metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic-Kaehler manifolds.