2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97612Periods of parallel exterior forms define natural coordinates on the deformation space of complete affine structures on the two-torus. These coordinates define a differentiable structure on this deformation space, under which it is diffeomorphic to $R^2$. The action of the mapping class group of $T^2$ is equivalent in these coordinates with the standard linear action of $\SL_2(Z)$ on $R^2$.26 pages, 9 figuresDifferential Geometry58D29,(22E40,22F30,57S30)text