Uwe Semmelmann (Stuttgart)
A well-known conjecture of LeBrun and Salamon states that quaternion Kähler manifolds of positive scalar curvature should be symmetric. This conjecture is still widely open. But even under the much stronger assumption of non-negative sectional curvature almost nothing is known.
In my talk I will present a new and very short proof of the analogous statement for Kähler manifolds, originally due to A. Gray. Moreover, I will explain why a proof of the conjecture in the quaternion Kähler case, given by Chow and Yang, is not correct. For this I will make a few remarks on the curvature of Wolf spaces and of twistor spaces of quaternion Kähler manifolds.
My talk is based on a recent preprint with Gregor Weingart and Oscar Macia.
