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In the field of [[mathematics]] known as [[differential geometry]], a '''generalized complex structure''' is a property of a [[differential manifold]] that includes as special cases a [[linear complex structure|complex structure]] and a [[symplectic structure]]. Generalized complex structures were introduced by [[Nigel Hitchin]] in 2002 and further developed by his students [[Marco Gualtieri]] and [[Gil Cavalcanti]].
These structures first arose in Hitchin's program of characterizing geometrical structures via [[functional (mathematics)|functional]]s of [[differential forms]], a connection which formed the basis of [[Robbert Dijkgraaf]], [[Sergei Gukov]], [[Andrew Nietzke]] and [[Cumrun Vafa]]'s 2004 proposal that [[topological string theory|topological string theories]] are special cases of a [[topological M-theory]]. Today generalized complex structures also play a leading role in physical [[string theory]], as [[supersymmetry|supersymmetric]] [[Compactification (physics)#Flux compactification|flux compactification]]s, which relate 10
==Definition==
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