Dual versions of extended supergravities

Recently, using the model of N = 2 supergravity — vector multiplets interaction with the scalar field geometry SU(1,m)SU(m) ⊗ U(1) as an example, we have shown that even when the scalar field geometry is fixed, one can have a whole family of Lagrangians, which differ by vector field duality transformation. In this paper we carry out the construction of such families for the case of N = 3 and N = 4 supergravities, the scalar field geometry being SU(3,m)SU(3) ⊗ SU(m) ⊗ U(1) and SU(1,1)U(1) ⊗ O(6,m)O(6) ⊗ O(m), correspondingly. Moreover, it turns out that these families contain, as a partial case, the models describing the interaction of an arbitrary number of vector multiplets with our hidden sectors, admitting spontaneous supersymmetry breaking without a cosmological term.