A quaternionic kähler manifold is a special type of Riemannian manifold equipped with a metric that is not only Kähler but also allows for the existence of a hypercomplex structure. This means it has a holonomy group that is a subgroup of the unitary group, specifically related to quaternionic structures. These manifolds play a significant role in the study of special holonomy, which is important in various areas of mathematics and theoretical physics.
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