Twistor theory for exceptional holonomy

TL;DR

This paper explores the application of twistor theory to manifolds with exceptional holonomy, specifically G_2 and Spin(7) manifolds, revealing natural Riemannian twistorial structures and reviewing related holonomy representations.

Contribution

It introduces natural Riemannian twistorial structures on G_2 and Spin(7) manifolds and reviews exceptional holonomy representations, advancing the geometric understanding of these special manifolds.

Findings

G_2 and Spin(7) manifolds possess natural Riemannian twistorial structures

Exceptional holonomy representations are reviewed and connected to twistorial geometry

Provides new insights into the geometric structures of special holonomy manifolds

Abstract

We show that the $G_2$-manifolds and certain ${\rm Spin}(7)$-manifolds are endowed with natural Riemannian twistorial structures. Along the way, the exceptional holonomy representations are reviewed and other related facts are considered.