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Almost complex manifold
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an almost complex manifold is a <a href="/facts/Smooth_manifold/aSnbXKcV">smooth manifold</a> equipped with a smooth <a href="/facts/Linear_complex_structure/gzGklcAX">linear complex structure</a> on each <a href="/facts/Tangent_space/crvpbSeG">tangent space</a>. Every <a href="/facts/Complex_manifold/DlvPnpzm">complex manifold</a> is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in <a href="/facts/Symplectic_geometry/runXFCea">symplectic geometry</a>. </p><p>The concept is due to <a href="/facts/Charles_Ehresmann/KNtePSlk">Charles Ehresmann</a> and <a href="/facts/Heinz_Hopf/PMks10NV">Heinz Hopf</a> in the 1940s. </p>