  Motivated by the ideas and methods used by Naitoh in the consideration of
parallel totally real submanifolds in complex space forms, the author of the
present paper successfully makes use of the so called Jordan triple and
(restricted) structure Lie algebra associated with a given Jordan algebra to
establish a one-to-one correspondence between the set of equivalence classes of
connected, simply connected and nondegenerate equiaffine symmetric
hypersurfaces with a given nonzero affine mean curvature and that of the
equivalence classes of semi-simple real Jordan algebras. Then, via the existing
classification theorem of the semi-simple real Jordan algebras with unity, a
complete classification for the nondegenerate and locally equiaffine symmetric
hypersurfaces with nonzero affine mean curvatures is established. As an direct
application of the main theorems, we prove at the end of the paper a complete
classification of nondegenerate hypersurfaces with parallel Fubini-Pick forms
and nonzero affine mean curvatures.
