4 problems

Spherical space form question. Must every closed manifold with harmonic curvature and $(n+\frac{n-2}{n})$-positive curvature operator of the second kind be diffeomorphic to a spher…

Böhm–Wilking's conjecture. For every $a\in[0,n/4]$, the curvature cone $\Omega(a)$ is invariant under the Hamilton ODE and preserved by Ricci flow.

Let $n$ be a dimension and let $\bigl\|W\bigr\|=1$ for a Weyl curvature operator $W\in\operatorname{Weyl}_n$. Define … and let…

Let $M^n$ be a closed $n$-dimensional Riemannian manifold, and let $n+\frac{n-2}{n}$ be the positivity threshold for its curvature operator of the second kind. Li's conjecture. If…