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  "body": "\n## Summary\n\nA hyperkähler manifold is a Riemannian manifold that is Kähler with respect to three complex structures $I$, $J$, $K$ that multiply like the quaternion units.\nIts dimension is a multiple of $4$, and its holonomy group lies in the compact symplectic group $Sp(n)$.\nHyperkähler manifolds are Ricci-flat, and they are one of the special holonomy cases in Berger's list.\nExamples include K3 surfaces with their Ricci-flat metrics and many moduli spaces from gauge theory.\n\n## Explanations\n\n### L1 human\n\nThe quaternions extend the complex numbers with three square roots of $-1$, called $i$, $j$ and $k$, with $ij = k$.\nA hyperkähler manifold lets one multiply tangent vectors by all three, in a way that respects lengths and stays the same when moved along curves.\nThe simplest example is the space $\\mathbb{H}^n$ of quaternion vectors with its flat metric.\nSo each such manifold is a complex manifold in many ways at once, one for each unit imaginary quaternion.\n",
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