  It has been shown recently that extended supersymmetry in twisted first-order
sigma models is related to twisted generalized complex geometry in the target.
In the general case there are additional algebraic and differential conditions
relating the twisted generalized complex structure and the geometrical data
defining the model. We study in the Hamiltonian formalism the case of vanishing
metric, which is the supersymmetric version of the WZ-Poisson sigma model. We
prove that the compatibility conditions reduce to an algebraic equation, which
represents a considerable simplification with respect to the general case. We
also show that this algebraic condition has a very natural geometrical
interpretation. In the derivation of these results the notion of contravariant
connections on twisted Poisson manifolds turns out to be very useful.
