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for some subbundle Δ. A point which has an [[open set|open]] [[neighborhood (mathematics)|neighborhood]] in which the dimension of the fibers of Δ is constant is said to be a '''regular point'''.
===Darboux's theorem===
{{main|Darboux's theorem}}
Every regular point in a generalized complex manifold has an open neighborhood which, after a diffeomorphism and shift of the B-field, has the same generalized complex structure as the [[Cartesian product]] of the [[Linear complex structure|complex vector space]] '''C'''<sup>k</sup> and the standard symplectic space '''R'''<sup>2n-2k</sup> with the standard symplectic form, which is the [[direct sum of matrices|direct sum]] of the two by two off-diagonal matrices with entries 1 and -1.
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