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In this paper, we study locally strongly convex centroaffine hypersurfaceswith parallel cubic form with respect to the Levi-Civita connection of thecentroaffine metric. As the main result, we obtain a complete classification ofsuch centroaffine hypersurfaces. The result of this paper is a centroaffineversion of the complete classification of locally strongly convex equiaffinehypersurfaces with parallel cubic form due to Hu, Li and Vrancken [12].

Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form