Reduction and submanifolds of generalized complex manifolds

We recall the presentation of the generalized, complex structures by classical tensor fields, while noticing that one has a similar presentation and the same integrability conditions for generalized, paracomplex and subtangent structures. This presentation shows that the generalized, complex, paracomplex and subtangent structures belong to the realm of Poisson geometry. Then, we prove geometric reduction theorems of Marsden–Ratiu and Marsden–Weinstein type for the mentioned generalized structures and give the characterization of the submanifolds that inherit an induced structure via the corresponding classical tensor fields.