In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criterion, we dualize the results to submersions and we make a few comments on generalized complex mappings. Then, we discuss submanifolds of generalized Kähler manifolds that have an induced generalized Kähler structure. These turn out to be the common invariant submanifolds of the two classical complex structures of the generalized Kähler manifold.
Bibliographical notePublisher Copyright:
© 2015, Springer-Verlag Wien.
- Bicomplex submanifold
- Generalized complex structure
- Generalized Kähler structure
- Induced structure
ASJC Scopus subject areas
- Mathematics (all)