3 problems

A positive quaternion-Kähler manifold is a complete quaternion-Kähler manifold $(M^{4n},g)$ with positive scalar curvature; the known examples are the Wolf spaces, which are compac…

Vanishing conjecture. For every positive quaternion-Kähler manifold different from $\mathbb{H}P^n$,

Let $(M,g)$ be a compact quaternion-Kähler spin manifold of dimension $4m\geq 8$. Such manifolds are Einstein, so their scalar curvature $S$ is constant. Let $\lambda$ be an eigenv…