A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of S p(n) S p(1) = S p(n)×S p(1)/Z_2, but is not a subgroup of S p(n). These manifolds are sometimes called quaternionic Kähler and are sometimes written hyphenated as quaternion-Kähler, quaternionic-Kähler, etc.

flat manifold | hyper-Kähler manifold | Kähler manifold | Riemannian manifold