  We first review standard results of the compactification of type IIA and IIB
supergravities on a Calabi-Yau threefold and illustrate mirror symmetry. Then
we compactify the same theories on a class of generalized Calabi-Yau manifolds
called Half-flat. We obtain the scalar potential, and we show that type IIA on
a Half-flat manifold is mirror symmetric to type IIB on a Calabi-Yau threefold
with electric NS-fluxes turned on. In the last part, we compute the full
equations of motion for N=4 supergravity in central charge superspace with the
graviphotons identified as central charge components of the vielbein. We show
the equivalence with the formulation in components.
