Twistor Theory for CR quaternionic manifolds and related structures

TL;DR

This paper introduces CR quaternionic manifolds, a broad class encompassing quaternionic and conformal manifolds, and develops their Twistor Theory along with a heaven space construction.

Contribution

It defines CR quaternionic manifolds in a non-metrical setting and establishes their Twistor Theory and heaven space construction, expanding the geometric framework.

Findings

CR quaternionic manifolds generalize quaternionic and conformal manifolds

A natural Twistor Theory is developed for these manifolds

Heaven space construction for quaternionic manifolds is obtained

Abstract

In a general and non metrical framework, we introduce the class of CR quaternionic manifolds containing the class of quaternionic manifolds, whilst in dimension three it particularizes to, essentially, give the conformal manifolds. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic manifolds.