Structures on manifolds | Complex manifolds

Hypercomplex manifold

In differential geometry, a hypercomplex manifold is a manifold with the tangent bundleequipped with an action by the algebra of quaternionsin such a way that the quaternions define integrable almost complex structures. If the almost complex structures are instead not assumed to be integrable, the manifold is called quaternionic, or almost hypercomplex. (Wikipedia).

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Tangent bundle | K3 surface | Manifold | Kähler manifold | Differential geometry | Quaternionic manifold | Almost complex manifold | Hyperkähler manifold | Affine connection | Hopf surface | Module (mathematics) | Charles Ehresmann | Twistor space