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Reduction of Courant algebroids and generalized complex structures. (English) Zbl 1115.53056

The authors study the reduction of generalized geometrical structures such as Dirac structures and generalized complex structures. Generally speaking, the quotient of a space does not inherit the same type of geometry as the original space; however it can be usefull to consider a reduction for this to occur. In this paper, the authors present a theory of reduction for Courant algebroids and Dirac structures. Extended actions and a generalized notion of moment map are then considered. Finally, generalized Kähler reduction is studied.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53D10 Contact manifolds (general theory)
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