Generalized complex submanifolds

Abstract


We introduce the notion of twisted generalized complex submanifolds and describe an
equivalent characterization in terms of Poisson–Dirac submanifolds. Our
characterization recovers a result of Vaisman (2007). An equivalent characterization
is also given in terms of spinors. As a consequence, we show that the fixed locus of an
involution preserving a twisted generalized complex structure is a twisted generalized
complex submanifold. We also prove that a twisted generalized complex
manifold has a natural Poisson structure. We also discuss generalized Kähler
submanifolds.


Keywords

generalized complex geometry, Poisson bivector, Poisson–Dirac submanifold

Mathematical Subject Classification

Primary: 53C56, 53D17, 53D35