Abstract
The compact complex manifolds considered in this article are principal torus bundles over a torus. We consider the Kodaira Spencer map of the complete Appell Humbert family (introduced by the first author in Part I) and are able to show that we obtain in this way a connected compo- nent of the space of complex structures each time that the base dimension is two, the fibre dimension is one, and a suitable topological condition is verified.
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