Almost $G_2$-manifolds with almost twistorial structures

TL;DR

This paper establishes the precise conditions under which the Penrose-Ward transformation can be applied to almost $G_2$-manifolds equipped with natural almost twistorial structures, advancing the understanding of their geometric properties.

Contribution

It provides the necessary and sufficient conditions for the Penrose-Ward transformation on almost $G_2$-manifolds with twistorial structures, a novel result in differential geometry.

Findings

Characterization of conditions for Penrose-Ward transformation

Extension of twistorial methods to almost $G_2$-manifolds

Enhanced understanding of geometric structures on $G_2$-manifolds

Abstract

We give the necessary and sufficient conditions for the Penrose-Ward transformation to work on almost $G_2$-manifolds, endowed with natural almost twistorial structures.