In this paper, we consider generalized moment maps forHamiltonian actions on H-twisted generalized complex manifolds introduced byLin and Tolman 15. The main purpose of this paper is to show convexity andconnectedness properties for generalized moment maps. We study Hamiltoniantorus actions on compact H-twisted generalized complex manifolds and provethat all components of the generalized moment map are Bott-Morse functions.Based on this, we shall show that the generalized moment maps have a conveximage and connected fibers. Furthermore, by applying the arguments of Lerman,Meinrenken, 'Tolman, and Woodward 13 we extend our results to the case ofHamiltonian actions of general compact Lie groups on H-twisted generalizedcomplex or bifolds.
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