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The classifications of locally strongly convex equiaffine hypersurfaces(resp. centroaffine hypersurfaces) with parallel Fubini-Pick form with respectto the Levi-Civita connection of the Blaschke-Berwald affine metric (resp.centroaffine metric) have been completed by several geometers in the lastdecades, see \cite{HLV} and \cite{CHM}. In this paper we define a generalizedCalabi product in Calabi geometry and prove decomposition theorems in terms oftheir Calabi invariants. As the main result, we obtain a completeclassification of Calabi hypersurfaces in $\bbr^{n+1}$ with parallelFubini-Pick form with respect to the Levi-Civita connection of the Calabimetric. This result is a counterpart in Calabi geometry of the classificationtheorems in equiaffine situation \cite{HLV} and centroaffine situation\cite{CHM}.

Classification of Calabi Hypersurfaces in $\bbr^{n+1}$ with parallel Fubini-Pick form