# Homogeneous 8-manifolds admitting invariant Spin(7)-structures

## TL;DR

This paper classifies compact, simply connected homogeneous 8-manifolds with invariant Spin(7)-structures, providing explicit examples, their types, and analyzing the associated Spin(7)-connection with torsion.

## Contribution

It offers a complete classification of such manifolds, explicit examples of invariant Spin(7)-structures, and analysis of their Spin(7)-connections with torsion.

## Key findings

- Classification of all canonical presentations G/H with invariant Spin(7)-structures
- Explicit examples of invariant Spin(7)-structures for each presentation
- Description of the type of Spin(7)-structures and analysis of associated connections

## Abstract

We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connected. For each presentation, we exhibit explicit examples of invariant Spin(7)-structures and we describe their type, according to Fern\'andez classification. Finally, we analyse the associated Spin(7)-connection with torsion.