5 problems

Higher-order vanishing conjecture. The component of the Einstein equation to order $4$ on $\Gamma(\operatorname{Sym}^{2,+}TM)$ should admit an analogue of the order-three identity,…

Folklore conjecture. Then $(X,g)$ is a homogeneous space.

Let $X$ be a Fano manifold with volume form $dV$, let $\beta_0<0$, and let $\beta$ range over the real numbers satisfying $\beta>\beta_0$. For each $N$, let $\mathcal{Z}_N(\beta)$…

Rotation-invariant classification conjecture. The only projectively induced and rotation-invariant Kähler–Einstein manifolds are open subsets of

Flag-manifold conjecture. If $(M,g)$ is a Kähler–Einstein manifold endowed with a projectively induced metric, then it is an open subset of a complex flag manifold.