Hyperkähler manifold
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In differential geometry, a hyperkähler manifold is a Riemannian manifold endowed with three integrable almost complex structures that are Kähler with respect to the Riemannian metric and satisfy the quaternionic relations . In particular, it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds.[lower-alpha 1]
Hyperkähler manifolds were defined by Eugenio Calabi in 1979.[1]