5 problems

Donald's conjecture. The structure $\underline{\omega}$ can be deformed through cohomologous hypersymplectic structures to the triple of Kähler forms arising from a hyperkähler met…

Donaldson's conjecture. For every such $M$ and $\underline{\omega}$, there exists a family with these properties.

Flatness conjecture. Every two-step nilpotent hypersymplectic Lie algebra is flat.

Donald'son conjecture. For every hypersymplectic structure $\underline{\omega}$ on a compact 4-manifold $M$, there is an isotopy $\underline{\omega}(t)$ of cohomologous hypersymple…

Donaldson's conjecture. There exists a deformation of $\underline{\omega}$ through cohomologous hypersymplectic structures to a hyperkähler triple. This conjecture asserts that, up…