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Reference.org
Hypercomplex manifold
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<p>In <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, a hypercomplex manifold is a <a href="/facts/Manifold/rXPERJtu">manifold</a> with the <a href="/facts/Tangent_bundle/dq8zW9Kb">tangent bundle</a> equipped with an <a href="/facts/Module_(mathematics)/jP0LIhFL">action</a> by <a href="/facts/Quaternions/T3tnu7mX">the algebra of quaternions</a> in such a way that the quaternions I , J , K {\displaystyle I,J,K} define integrable <a href="/facts/Almost_complex_manifold/wsXTsuC6">almost complex structures</a>. </p><p>If the almost complex structures are instead not assumed to be integrable, the manifold is called quaternionic, or almost hypercomplex. </p>