In differential geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex structures I , J , K {\displaystyle I,J,K} that are Kähler with respect to the Riemannian metric g {\displaystyle g} and satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − 1 {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1} . In particular, it is a hypercomplex manifold.
In differential geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex structures I , J , K {\displaystyle I,J,K} that are Kähler with respect to the Riemannian metric g {\displaystyle g} and satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − 1 {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1} . In particular, it is a hypercomplex manifold.
Source: Wikipedia "Hyperkähler manifold" · CC BY-SA 4.0
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