# Spinorial classification of Spin(7) structures

## TL;DR

This paper classifies Spin(7) structures using spinorial equations, relates them to G2 structures, and analyzes invariant structures on quasi abelian Lie algebras, providing a unified spinorial framework.

## Contribution

It introduces a spinorial classification of Spin(7) structures and connects them to G2 structures, with applications to invariant structures on specific Lie algebras.

## Key findings

- Classified Spin(7) structures via spinorial equations
- Linked Spin(7) and G2 structures in certain geometries
- Analyzed invariant Spin(7) structures on quasi abelian Lie algebras

## Abstract

We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze invariant $\mathrm{Spin(7)}$ structures on quasi abelian Lie algebras.

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Source: https://tomesphere.com/paper/1803.08734