Stationary values of sectional curvature in Grassmanian manifolds of bivectors

In the Grassmanian manifold $G^+_{2,n}$ of bivectors $(n\ge4)$ the curvature $K(\sigma)$ of the section on direction of a flat area $\sigma$ takes values on the range from 0 to 2. All stationary values $a$ of the function $K(\sigma)$ such that the gradient $\nabla K\big|_{\sigma=\sigma_0}=0$ for at least one $\sigma_0\in K^{-1}(a)$ are found. Those values are $\{0,1,2\}$ for $n=4$, $\{0,1/5,1,2\}$ for $n=5$, $\{0,1/5,1/2,1,2\}$ for $n\ge6$.