3 problems

Hermitianity conjecture. Any ALF instanton must be Hermitian, either Kähler or non-Kähler.

Let $M$ be the total space of $\mathcal{O}(1)$ over $\mathbb{CP}^1$, equipped with an $\operatorname{ALF}$-$A_k$ gravitational-instanton metric $g$. Taub-Bolt uniqueness conjecture…

Let $k\geq 0$, and let $(M,g)$ be an $\operatorname{ALF}$-$A_k$ gravitational instanton. ALF-$A_k$ uniqueness conjecture. Up to isometry, scaling, and orientation reversal, $(M,g)$…