An Ansatz for Hyperkähler $8$-Manifolds with two Commuting Rotating Killing Fields

Joseph Malkoun

We consider a hyperkähler $8$-manifold admitting either a $U(1)\times \mathbb{R}$, or a $U(1)\times U(1)$ action, where the first factor preserves $g$ and $I$, and acts on $ω_2+i…