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  "body": "\n## Summary\n\nA quaternion-Kähler manifold is a Riemannian manifold of dimension $4n$ whose holonomy group lies in $Sp(n) \\cdot Sp(1)$.\nLocally it carries three almost complex structures that multiply like the quaternion units.\nParallel transport preserves the bundle they span, but not each of them.\nFor $n \\ge 2$ such manifolds are Einstein, and despite the name they are in general not Kähler.\nQuaternionic projective space $\\mathbb{H}P^n$ is the basic example.\n\n## Explanations\n\n### L1 human\n\nA [[hyperkähler manifold|87AWY7NQS0]] has three fixed ways to multiply by quaternion units.\nIn a quaternion-Kähler manifold the three ways may rotate among themselves as one moves around the manifold.\nOnly the three-dimensional family they span is well defined.\nThe quaternionic projective space, the quaternion analogue of the complex projective space, is the model example.\n",
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