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

On the symmetric equiaffine hyperspheres and the minimal symmetric Lagrangian submanifolds