  In this paper, a correspondence via duality is established between the set of
locally strongly convex symmetric equiaffine hyperspheres and the set of
minimal symmetric Lagrangian submanifolds in a certain complex space form. By
using this correspondence theorem, we are able to provide an alternative proof
of the classification theorem for the locally strongly convex equiaffine
hypersurfaces with parallel Fubini-Pick forms, which has been established
recently by Z.J. Hu etc in a totally different way.
