 A Dirac structure is a maximally isotropic subbundle of formula_5 whose sections are closed under the Courant bracket.Dirac structures include as special cases symplectic structures, Poisson structures and foliated geometries.A generalized complex structure is defined identically, but one tensors formula_5 by the complex numbers and uses the complex dimension in the above definitions and one imposes that the direct sum of the subbundle and its complex conjugate be the entire original bundle (Tformula_13
T*)formula_14C.