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

Authors