The stability of Yang-Mills connections on $\delta$-pinched manifolds

Abstract

In this article, we establish pinching conditions under which all weakly stable Yang-Mills connections on compact manifolds are flat. As a corollary, we provide a dimension-dependent constant $\delta(n)$ and prove that there exist no non-flat weakly stable Yang-Mills connections on $\delta(n)$-pinched compact simply-connected Riemannian manifolds.