We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define extended actions and a generalized notion of moment map. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on C P2. © 2006 Elsevier Inc. All rights reserved.
Bursztyn, H., Cavalcanti, G. R., & Gualtieri, M. (2007). Reduction of Courant algebroids and generalized complex structures. Advances in Mathematics, 211(2), 726–765. https://doi.org/10.1016/j.aim.2006.09.008