Contents

Ingredients

Concepts

Constructions

Examples

Theorems

# Contents

## Idea

A space which is both a quaternion-Kähler manifold as well as a symmetric space. Also known as a Wolf space.

## Properties

### As positive quaternion-Kähler manifolds

under construction

###### Proposition

In fact the Wolf spaces are the only known examples of positive quaternion-Kähler manifold (which is not hyper-Kähler ?!), as of today (e.g. Salamon 82, Section 5).

This leads to the conjecture that un every dimension, the Wolf spaces are the only positive quaternion-Kähler manifolds.

The conjecture has been proven for the following dimensions