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holomorphic tangent space
In mathematics, specifically in the field of complex geometry, the holomorphic tangent space of a complex manifold ''M'' is the tangent space of the smooth manifold Σ underlying ''M'' viewed as complex vector space via the almost complex structure ''J'' of ''M''. The holomorphic tangent bundle (''T''Σ, ''J'') is isomorphic to a subbundle of the complexification of the real tangent bundle, namely the eigenbundle of ''J'' for the eigenvalue +''i'' (compare linear complex structure). The holomorphic tangent bundle is often denoted by ''T''(1,0)''M''.
==See also==
*Almost complex manifold
*Hermitian manifold
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