In this paper, we consider generalized moment maps for Hamiltonian actions on H-twisted generalized complex manifolds introduced by Lin and Tolman . The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact H-twisted generalized complex manifolds and prove that all components of the generalized moment map are Bott-Morse functions. Based on this, we shall show that the generalized moment maps have a convex image and connected fibers. Furthermore, by applying the arguments of Lerman, Meinrenken, Tolman, and Woodward  we extend our results to the case of Hamiltonian actions of general compact Lie groups on H-twisted generalized complex orbifolds.
- Convexity properties
- Generalized complex structures
- Moment maps