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

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.