Ricci flow unstable cell centered at an Einstein metric on the twistor space of positive quaternion K\"ahler manifolds of dimension $\geq 8$

TL;DR

This paper demonstrates that ancient solutions to Ricci flow, derived from the twistor space of positive quaternion Kähler manifolds, can be used to classify these manifolds as Wolf spaces, revealing their geometric structure.

Contribution

It introduces a novel application of Ricci flow ancient solutions to classify positive quaternion Kähler manifolds as Wolf spaces.

Findings

Ancient Ricci flow solutions arise from twistor space collapsings.

These solutions help classify positive quaternion Kähler manifolds.

The classification confirms the manifolds are Wolf spaces.

Abstract

We show that a 1-parameter family Ricci flow ancient solutions arises from the natural collapsings of the twistor space of positive quaternion K\"ahler manifolds. We use these ancient solutions to show that a positive quaternion K\"ahler manifold is isometric to one of the Wolf spaces.