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where <math>\mathcal{L}_X</math> is the [[Lie derivative]] along the vector field ''X'', ''d'' is the [[exterior derivative]] and ''i'' is the [[Exterior algebra#The interior product or insertion operator|interior product]].
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A '''generalized complex structure''' is a generalized almost complex structure such that the space of smooth sections of ''L'' is closed under the Courant bracket.
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