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arXiv · 1409.7799

An Ansatz for Hyperk\"ahler $8$-Manifolds with two Commuting Rotating Killing Fields

Joseph Malkoun
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Abstract

We consider a hyperk\"{a}hler $8$-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 $\omega_2+i\omega_3$ by multiplying it by itself, while the second factor preserves $g$ and acts triholomorphically. Such data can be reduced to a single function $H$ of two complex variables and two real variables satisfying $6$ equations of Monge-Ampere type, which can be compactly written down using a Poisson bracket.

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Joseph Malkoun. 2014-09-27. An Ansatz for Hyperk\"ahler $8$-Manifolds with two Commuting Rotating Killing Fields. https://arxiv.org/abs/1409.7799

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